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 <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vs = vector<string>;
using pll = pair<ll, ll>;
using vp = vector<pll>;
#define rep(i, n) for(ll i = 0; i < (n); i++)
#define repr(i, a, b) for(ll i = (a); i < (b); i++)
#define ALL(a) (a).begin(), (a).end()
#define SZ(x) ((ll)(x).size())
const ll MOD = 1000000007;
const ll INF = 100000000000000000LL;
inline ll GCD(ll a, ll b){ return b?GCD(b, a % b):a; }
inline ll LCM(ll a, ll b){ return a/GCD(a, b)*b; }
inline ll powint(ll x, ll y){ ll r=1; while(y){ if(y&1) r*=x; x*=x; y>>=1; } return r; }
inline ll powmod(ll x, ll y, ll m = MOD){ ll r=1; while(y){ if(y&1) r*=x; x*=x; r%=m; x%=m; y>>=1; } return r; }
template<class T>bool chmax(T &a, const T &b){ if(a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b){ if(b<a) { a=b; return 1; } return 0; }
#ifdef OJ_LOCAL
#include "dump.hpp"
#else
#define dump(...) ((void)0)
#endif

vll p{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 57, 71, 73, 79, 83, 89, 97};
vll fac(101, 0);

void fact(ll n){
    ll i = 2;
    while(n >= 2){
        if(n % i == 0){
            n /= i;
            fac[i]++;
            i = 2;
        }else{
            i++;
        }
    }
}

int main(){
    cin.tie(0); ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    ll n;
    cin >> n;
    repr(i, 1, n+1){
        fact(i);
    }
    ll ans = 0;
    rep(i, 101)repr(j, i+1, 101)rep(k, 101){
        if(j == k || k == i) continue;
        if(fac[i] >= 4 && fac[j] >= 4 && fac[k] >= 2) ans++;
    }
    rep(i, 101)rep(j, 101){
        if(i == j) continue;
        if(fac[i] >= 14 && fac[j] >= 4) ans++;
        if(fac[i] >= 24 && fac[j] >= 2) ans++;
    }
    rep(i, 101){
        if(fac[i] >= 74) ans++;
    }
    cout << ans << endl;
    return 0;
}