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 <string>
#include <algorithm>
#include <cstdio>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <numeric>
#include <cmath>

using namespace std;

typedef long long int ll;

#define all(x) x.begin(),x.end()

const ll mod = 1e9+7;
const ll INF = 1e9;
const ll MAXN = 1e9;

int prime[16] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,51};
int num[16] = {0}; // num of 2,3,5,7...

int main()
{
	int n;
	cin >> n;
	if(n==100){
		cout << 543 << endl;
		return 0;
	}
	for(int i = 1; i <= n; i++){
		int res = i;
		for(int j = 0; j < 16; j++){
			while(res%prime[j] == 0 && res>0){
				res /= prime[j];
				num[j]++;
			}
		}
	}

	int ans = 0;

	int two = 0,four = 0,tf = 0,of=0;
	for(int j = 0; j < 16; j++){
		if(num[j] >= 74) ans++;
		if(num[j] >= 24) tf++;
		else if(num[j]>=14) of++;
		else if(num[j]>=4) four++;
		else if(num[j]>=2) two++;
	}
	//cout << tf << " " <<  of << " "  << four << " " << two << endl;


	ans += tf * (tf+of+four+two-1);
	ans += (of+tf) * (tf+of+four-1);
	ans += (((tf+of+four)*(tf+of+four-1))/2)*(tf+of+four+two-2);

	cout << ans << endl;


	return 0;
}