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<algorithm>
#include<string>
#include<sstream>
using namespace std;
int main() {
  int n;
  cin >> n;
  stringstream ss;
  bool* prime = new bool[101];
  for(int i=0;i<101;i++) prime[i] = true;
  prime[0] = false;
  prime[1] = false;
  for(int i=2;i<101;i++){
    if(!prime[i])continue;
    for(int j=i*2;j<101;j+=i){
      prime[j] = false;
    }
  }
  //cout << "prime end" << endl;
  int* table = new int[101];
  for(int i=0;i<101;i++) table[i] = 0;
  for(int i=1;i<n+1;i++){
    int c = i;
    while(c>1){
      for(int j=2;j<101;j++){
        if(prime[j] && c%j==0){
          table[j] ++;
          c /= j;
        }
      }
      //cout << i << endl;
    }
  }
  //cout << "table end" << endl;
  int ans =0;
  int diff = 0;

  int count1=0;
  int count2=0;
  for(int i=0;i<101;i++){
    if(table[i]>=74) count2++;
  }
  diff = count2;
  ans += diff;
  //cout << "74: " << diff << endl;

  count1=0;
  count2=0;
  diff=0;
  for(int i=0;i<101;i++){
    if(table[i]>=4) count2++;
    else if(table[i]>=2) count1++;
  }
  diff += count1*count2*(count2 - 1)/2;
  diff += count2*(count2-1)*(count2-2)/2;
  ans += diff;
  //cout << "2,4,4: " << diff << endl;

  count1=0;
  count2=0;
  diff=0;
  for(int i=0;i<101;i++){
    if(table[i]>=24) count2++;
    else if(table[i]>=2) count1++;
  }
  diff += count1*count2;
  diff += count2*(count2-1);
  ans += diff;
  //cout << "2,24: " << diff << endl;

  count1=0;
  count2=0;
  diff=0;
  for(int i=0;i<101;i++){
    if(table[i]>=14) count2++;
    else if(table[i]>=4) count1++;
  }
  diff += count1*count2;
  diff += count2*(count2-1);
  ans += diff;
  //cout << "4,14 " << diff << endl;

  count1=0;
  count2=0;
  diff=0;
  //for(int i=1;i<n+1;i++){
  //  if(table[i]!=0)cout << i << " : " << table[i] << endl;
  //}
  //cout << table[0] << endl;

  cout << ans << endl;
  return 0;
}