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)

#include<stdio.h>
#include <cstdio>
#include <iostream>
#include <iomanip>
#include <string>
#include <algorithm>
#include <vector>
#include <math.h>
#include<stack>
#include <queue>
#include<map>
#include <set>
#include<math.h>
using namespace std;
#define int long long
#define ll long long
#define rep(i,n) for(ll i=0;i<n;++i)
#define loop(i,m,n) for(ll i=m;i<n;++i)
#define ggr getchar(); getchar();return 0;
#define pie 3.141592653589793238462643383279
#define elif else if
#define P pair<ll,ll>
const int inf = 1000000007;
int bin(int bina) {
	int ans = 0;
	for (int i = 0; bina > 0; i++)
	{
		ans = ans + (bina % 2) * pow(10, i);
		bina = bina / 2;
	}
	return ans;
}
bool prime(int n) {
	for (ll i = 2; i <= sqrt(n); i++) {
		if (n % i == 0)return false;
	}
	return n != 1;
}
int gcd(int x, int y) {
	if (y == 0)return x;
	return gcd(y, x % y);
}
int lcm(int x, int y) {
	return x * y / gcd(x, y);
}
int kai(int x) {
	if (x == 0)return 1;
	return kai(x - 1) * x % inf;
}
int mod_pow(int x, int y, int mod) {
	int res = 1;
	while (y > 0) {
		if (y & 1) {
			res = res * x % mod;
		}
		x = x * x % mod;
		y >>= 1;
	}
	return res;
}
int comb(int x, int y) {
	return kai(x)* mod_pow(kai(x - y), inf - 2, inf) % inf * mod_pow(kai(y), inf - 2, inf) % inf;
}
struct union_find {
	int par[200010], size_[200010];
	void init(int x) {
		rep(i, x) { par[i] = i; size_[i] = 1; }
	}
	int find(int x) {
		if (par[x] == x)return x;
		return par[x] = find(par[x]);
	}
	void unite(int x, int y) {
		x = find(x); y = find(y);
		if (x == y)return;
		if (size_[x] < size_[y]) {
			par[x] = y;
			size_[y] += size_[x];
		}
		else {
			par[y] = x;
			size_[x] += size_[y];
		}
	}
};
map<int, int>mp;
int s[105],ans;
signed main() {	
	int n;
	cin >> n;
	loop(i, 2, n) {
		if (!prime(i))continue;
		int a = n, cnt = 0;
		while (a) {
			cnt += a / i;
			a /= i;
		}
		mp[cnt]++;
	}
	for (int i = 100; i >= 2; i--) {
		s[i] = mp[i] + s[i + 1];
	}
	ans += s[74];
	ans += s[24] * (s[2] - 1);
	ans += s[14] * (s[4] - 1);
	ans += (s[4] * (s[4] - 1)) / 2 * (s[2] - 2);
	cout << ans << endl;
}