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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[101];
        for (int i = 2 ; i <= n; i++) {
            int d = i;
            for (int j = 2 ; j <= i ; j++) {
                if (d == 1) {
                    break;
                }
                while (d > 1) {
                    if (d % j == 0) {
                        a[j]++;
                        d /= j;
                    } else {
                        break;
                    }
                }
            }
        }

        int over2 = 0;
        for (int i = 0 ; i < 101; i++) {
            if (a[i] >=  2) {
                over2++;
            }
        }
        int over4 = 0;
        for (int i = 0 ; i < 101; i++) {
            if (a[i] >=  4) {
                over4++;
            }
        }
        int over14 = 0;
        for (int i = 0 ; i < 101; i++) {
            if (a[i] >=  14) {
                over14++;
            }
        }
        int over24 = 0;
        for (int i = 0 ; i < 101; i++) {
            if (a[i] >=  24) {
                over24++;
            }
        }
        int over74 = 0;
        for (int i = 0 ; i < 101; i++) {
            if (a[i] >=  74) {
                over74++;
            }
        }
        int ans = 0;
        //3*5*5
        ans += over4 * (over4 - 1)/ 2 * (over2 - 2);
         //5*15
        ans += over14 * (over4 - 1);
        //3*25
        ans += over24 * (over2 - 1);
        //75
        ans += over74;

        System.out.println(ans);


    }

}