Problem:
Score : 200 points

Problem Statement

You are given a positive integer X.
Find the largest perfect power that is at most X.
Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.

Constraints

1 ≤ X ≤ 1000

X is an integer.

Input

Input is given from Standard Input in the following format:

X

Output

Print the largest perfect power that is at most X.

Sample Input 1

10

Sample Output 1

9

There are four perfect powers that are at most 10: 1, 4, 8 and 9.
We should print the largest among them, 9.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

999

Sample Output 3

961

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
 
int main() {
  int x;
  cin >> x;
  vector<int> v;
  v.push_back(1);
  for (int i = 2; i <= 31; i++){
    int p = 2;
    while(1){
      int num = pow(i, p);
      if (num <= 1000) {
        v.push_back(num);
        p++;
      } else {
        break;
      }
    }
  }
  v.push_back(1001);
  sort(v.begin(), v.end());
  for (int i = 0; i < v.size(); i++){
    if (x < v[i]){
      cout << v[i-1] << endl;
      return 0;
    }
  } 
}