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 <iostream>
#include <vector>
#include <unordered_map>
#include <algorithm>
using namespace std;
typedef long long ll;

int calc(vector<int> &cnt, int bits, int rest, int pos) {
	//cout << bits << "," << rest << endl;
	int ret = 0;
	for(int i = 3; i < rest; i++) {
		if(rest%i==0) {
			for(int j = pos; j < cnt.size(); j++) {
				if(cnt[j]>=(i-1)&&((bits&(1<<j))==0)) {
					ret += calc(cnt,bits|(1<<j),rest/i,j+1);
				}
			}
		}
	}
	for(int i = pos; i < cnt.size(); i++) {
		if(cnt[i]>=(rest-1)&&(((bits&(1<<i))==0))) {
			ret++;
		}
	}
	//cout << bits << "," << rest << " = " << ret << endl;
	return ret;
}

int main() {
	int n;
	cin >> n;
	unordered_map<int,int> mp;
	for(int i = 2; i <= n; i++) {
		int temp = i;
		while(temp>1) {
			for(int j = 2; j <= i; j++) {
				if(temp%j==0) {
					temp/=j;
					mp[j]++;
					break;
				}
			}
		}
	}
	vector<int> cnt;
	for(pair<int,int> p : mp) {
		//cout << "  " << (p.first) << "," << (p.second) << endl;
		cnt.push_back(p.second);
	}
	sort(cnt.begin(),cnt.end());
	cout << calc(cnt,0,75,0) << endl;
	return 0;
}