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: Runtime Error)

#include<bits/stdc++.h>

using namespace std;
using ll = long long;

map<int,int> Map;
template<class T>
void fact(T n){
    for(T i = 2; i * i <= n; i++){
        while(n % i == 0){
            Map[i]++;
            n /= i;
        }
    }
    if(n == 1)return;
    Map[n]++;
}


int main()
{
    int n;
    cin >> n;
    for(int i = 1; i <= n; i++) fact(i);
    int res = 0;
    vector<int> num;
    for(auto i : Map)num.push_back(i.second);
    int m = num.size();

    for(int i = 0; i < m; i++) {
        for(int j = i + 1; j < m; j++) {
            for(int k = 0; k < m; k++) {
                if(i == k || j == k)continue;
                if(num[i] >= 4 && num[j] >= 4 && num[k] >= 2)res++;
            }
        }
    }

    for(int i = 0; i < m; i++) {
        for(int j = 0; j < m; j++) {
            if(i == j)continue;
            if(num[i] >= 14 && num[j] >= 4)res++;
        }
    }

    for(int i = 0; i < m; i++) {
        for(int j = 0; j < m; j++) {
            if(i == j)continue;
            if(num[i] >= 24 && num[j] >= 2)res++;
        }
    }
    if(num.front() >= 74)res++;
    
    
    cout << res << endl;
}