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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
int main(){
  int X;
  cin >>X;
  //縺ｹ縺堺ｹ玲焚縺ｧ縺ゅｋ縺・
  vector<bool> expo(X+1);
  expo[1] = true;
  //2縺九ｉx縺ｾ縺ｧ
  for(int b=2;b<=X;b++){
    int v = b*b;
    while(v<=X){
      expo[v] = true;
      v *= b;
    }
  }

  //陦ｨ遉ｺ
  for(int i=X;i>=1;i--) if(expo[i]) cout <<i<<endl;
}