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 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cmath>
using namespace std;

int main(){
  int X;
  bool ans[1001];
  for(int i=0;i<1001;i++) ans[i] = false;
  ans[1] == true;
  for(int p=2;p<10;p++){
    for(int b=1;(int)pow(b,p)<1001;b++){
      ans[(int)pow(b,p)] = true;
    }
  }
  cin >> X;
  while(true){
    if(ans[X]){
      cout << X << endl;
      break;
    }
    X--;
  } 
  return 0;
}