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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
using LL = long long;
using ULL = unsigned long long;
#define rep(i,n) for(int i=0; i<(n); i++)

int main() {
    int N; cin >> N;
    vector<int> P;
    for (int i = 2; i <= N; i++) {
        bool ok = true;
        for (int p : P) if (i % p == 0) ok = false;
        if (ok)P.push_back(i);
    }

    vector<int> I(P.size());
    rep(i, P.size()) {
        int n = N, p = P[i];
        while (n >= p) { I[i] += n / p; n /= p; }
    }

    int ans = 0;

    rep(i, I.size()) rep(j, I.size()) rep(k, I.size()) {
        if (i == j || j == k || i == k) continue;
        if (I[i] < 4 || I[j] < 4 || I[k] < 2) continue;
        if (i > j) continue;
        ans++;
    }
    rep(i, I.size()) rep(j, I.size()){
        if (i == j) continue;
        if (I[i] < 14 || I[j] < 4) continue;
        ans++;
    }
    rep(i, I.size()) rep(j, I.size()) {
        if (i == j) continue;
        if (I[i] < 24 || I[j] < 2) continue;
        ans++;
    }
    rep(i, I.size()) {
        if (I[i] < 74) continue;
        ans++;
    }

    cout << ans << endl;

    return 0;
}