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.RegularExpressions;
using static kyoupuro.Input;
using static kyoupuro.MyMath;
using static kyoupuro.Modular;

namespace kyoupuro {

    class MainClass {

        public static void Main() {
            var N = NextInt;
            var array = new int[100];
            int count = 0;

            for (int i = 2; i <= N; i++) {
                int num = i;
                for (int j = 2; j < 100 && j != 1; j++) {
                    while(num % j == 0) {
                        num /= j;
                        array[j]++;
                    }
                }
            }

            int two = array.Count(x => x >= 2);
            int four = array.Count(x => x >= 4);
            int fourteen = array.Count(x => x >= 14);
            int twfour = array.Count(x => x >= 24);
            int svfour = array.Count(x => x >= 74);
            int tmp;

            // 5 * 5 * 3
            tmp = ((four * (four - 1)) / 2) * (two - 2);
            if(tmp > 0) {
                count += tmp;
            }

            // 15 * 5
            tmp = fourteen * (four - 1);
            if (tmp > 0) {
                count += tmp;
            }

            // 25 * 3
            tmp = twfour * (two - 1);
            if (tmp > 0) {
                count += tmp;
            }

            // 75
            tmp = svfour;
            if (tmp > 0) {
                count += tmp;
            }
                
            Console.WriteLine(count);
        }
    }

    class MyMath {
        public static long Gcd(long a, long b) {
            return b == 0 ? a : Gcd(b, a % b);
        }

        public static long Sqrt(long n) {
            if (n < 0) return 0;
            long a = 0, tmp = 0, b = 0;
            for (int i = 62; i >= 0; i -= 2) {
                tmp = (b << 1) + 1 <= (n >> i) ? 1 : 0;
                a = a << 1 | tmp;
                n -= (((b << 1) + 1) * tmp) << i;
                b = (b << 1) + tmp + tmp;
            }
            return a;
        }
    }

    class Modular {
        public const int mod = 1000000007;
        public readonly long value;
        public Modular(long value) { this.value = value; }
        public static implicit operator Modular(long a) {
            var m = a % mod;
            return new Modular((m < 0) ? m + mod : m);
        }
        public static Modular operator +(Modular a, Modular b) {
            return a.value + b.value;
        }
        public static Modular operator -(Modular a, Modular b) {
            return a.value - b.value;
        }
        public static Modular operator *(Modular a, Modular b) {
            return a.value * b.value;
        }
        private static Modular Pow(Modular a, int n) {
            switch (n) {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular operator /(Modular a, Modular b) {
            return a * Pow(b, mod - 2);
        }
        private static readonly List<int> facs = new List<int> { 1 };
        private static Modular Fac(int n) {
            for (int i = facs.Count; i <= n; ++i) {
                facs.Add((int)(Math.BigMul(facs.Last(), i) % mod));
            }
            return facs[n];
        }
        public static Modular Ncr(int n, int r) {
            return (n < r) ? 0
                 : (n == r) ? 1
                            : Fac(n) / (Fac(r) * Fac(n - r));
        }
        public static explicit operator int(Modular a) {
            return (int)a.value;
        }
    }

    public class PriorityQueue<T> {

        readonly List<T> _heap = new List<T>();
        readonly Comparison<T> _comparison;

        public PriorityQueue(Comparison<T> comparison) {
            _comparison = comparison;
        }

        public PriorityQueue() : this(Comparer<T>.Default.Compare) { }

        public PriorityQueue(IComparer<T> comparer) : this(comparer.Compare) { }

        public void Enqueue(T item) {
            _heap.Add(item);

            int childID = _heap.Count - 1;
            int parentID = (childID - 1) / 2;

            while (childID > 0 && _comparison(_heap[parentID], _heap[childID]) > 0) {
                Swap(parentID, childID);
                childID = parentID;
                parentID = (parentID - 1) / 2;
            }
        }

        public T Dequeue() {
            var first = _heap.First();
            _heap[0] = _heap.Last();
            _heap.RemoveAt(_heap.Count - 1);

            int parentID = 0;
            int childID = parentID * 2 + 2;
            if (childID >= _heap.Count || _comparison(_heap[childID], _heap[childID - 1]) > 0) childID--;

            while (childID < _heap.Count && _comparison(_heap[parentID], _heap[childID]) > 0) {
                Swap(parentID, childID);
                parentID = childID;
                childID = parentID * 2 + 2;
                if (childID >= _heap.Count || _comparison(_heap[childID], _heap[childID - 1]) > 0) childID--;
            }

            return first;
        }

        void Swap(int parent, int child) {
            var tmp = _heap[parent];
            _heap[parent] = _heap[child];
            _heap[child] = tmp;
        }

        public T Peek() { return _heap[0]; }
        public int Count => _heap.Count;
        public bool Any() { return _heap.Any(); }
        public List<T> Data => _heap;
    }

    public class UnionFind {
        public int[] Parents { get; set; }
        public UnionFind(int size) {
            Parents = Enumerable.Repeat(-1, size).ToArray();
        }

        public int Find(int num) {
            if (Parents[num] < 0) return num;

            Parents[num] = Find(Parents[num]);
            return Parents[num];
        }

        public int Size(int num) {
            return -Parents[Find(num)];
        }

        public bool Same(int a, int b) {
            return Find(a) == Find(b);
        }

        public void Unite(int a, int b) {
            int x = Find(a), y = Find(b);

            if (Size(x) > Size(y)) {
                Parents[x] += Parents[y];
                Parents[y] = x;
            } else {
                Parents[y] += Parents[x];
                Parents[x] = y;
            }
        }
    }

    class Input {
        static IEnumerator<string> enumerator = new string[] { }.AsEnumerable().GetEnumerator();

        public static string Line => Console.ReadLine();

        public static string[] StrArr => Line.Split(' ');

        public static int NextInt => int.Parse(NextWord());

        public static long NextLong => long.Parse(NextWord());

        public static List<int> IntList => StrArr.Select(int.Parse).ToList();

        public static List<long> LongList => StrArr.Select(long.Parse).ToList();

        public static string NextWord() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr.AsEnumerable().GetEnumerator();
            }
            return enumerator.Current;
        }
    }
}