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++14 (GCC 5.4.1) (judge verdict: Accepted)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author win11905
 */

#include <bits/stdc++.h>
#define all(x) (x).begin(), (x).end()
#define long long long
#define pii pair<int, int>
#define x first
#define y second
using namespace std;
const long MOD = 1e9+7, LINF = 1e18 + 1e16;
const int INF = 1e9+1;
const double EPS = 1e-10;
const int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};


class TaskD {
private:
    int n, c3, c5, c15, c25, c75;
    vector<int> prime;
public:
	void solve(istream& cin, ostream& cout) {
	    cin >> n;
        for(int i = 2; i <= 100; ++i) {
            bool st = true;
            for(int j = 2; j < i; ++j) if(i % j == 0) st = false;
            if(st) prime.emplace_back(i);
        }
        for(auto x : prime) {
            int cnt = 0;
            for(int i = 2; i <= n; ++i) {
                int z = i;
                while(z % x == 0) z /= x, cnt++;
            }
            if(cnt >= 2) c3++;
            if(cnt >= 4) c5++;
            if(cnt >= 14) c15++;
            if(cnt >= 24) c25++;
            if(cnt >= 74) c75++;
        }
        int ans = 0;
        ans += c5 * (c5 - 1) / 2 * (c3 - 2);
        ans += c15 * (c5 - 1);
        ans += c25 * (c3 - 1);
        ans += c75;
        cout << ans << endl;
	}
};

class Solver {
public:
	void solve(std::istream& in, std::ostream& out) {
		TaskD *obj = new TaskD();
		obj->solve(in, out);
	}
};

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	Solver solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}