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: Wrong Answer)

#include <stdio.h>
#include <iostream>
#include <vector>
#include <string>
#include <math.h>
#include <algorithm>
using namespace std;
typedef int ll;

vector<ll> d(101,1);

void zz(int a,int b){
  if(a>0){
    if(a%b){
      d[a]++;
      a/=b;
      zz(a,b);
    }
  }
}

int main(){
  ll n;
  cin>>n;
  vector<int> res;
  vector<bool> is_prime(n + 1, true);
  for (int p = 2; p <= n; p++) {
      if (!is_prime[p]) continue;
      // p の倍数を全て消す。
      for (int k = p * 2; k <= n; k += p) is_prime[k] = false;
      res.push_back(p);
  }
  vector<vector<ll> > dp(n+1,vector<ll>(0,0));
  vector<ll> dpp(101,0);
  for(int i=2;i<=n;i++){
    for(int j=2;j<=i;j++){
      if(is_prime[j]){
        zz(i,j);
      }
    }
  }
  for(int i=1;i<=n;i++){
    if(d[i]>=25) dpp[25]++;
    else if(d[i]>=15) dpp[15]++;
    else if(d[i]>=5) dpp[5]++;
    else if(d[i]>=3) dpp[3]++;
  }
  ll ans=0;
  ans+=(dpp[25]*(dpp[15]+dpp[3]+dpp[5]+max((dpp[25]-1),0)));
  ans+=(dpp[15]*(max((dpp[15]-1),0)+dpp[5]+dpp[25]));
  ans+=(dpp[5]*(dpp[5]-1)/2*(max((dpp[5]-2),0)+dpp[3]+dpp[15]+dpp[25]));
  cout<<ans<<endl;
}