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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < (n); i++)
using ll = long long;
using ull = unsigned long long;
using P = pair<int,int>;
using PP = pair<int,pair<int,int>>;
using T = tuple<string,int,int>;
const ll INF = 1LL<<60;

int main(){
  int x; cin >> x;
  vector<bool> chk(x+1);
  chk[1] = 1;
  for(int i = 2; i <= x; i++){
    int now = i*i;
    while(now <= x){
      chk[now] = true;
      now *= i;
    }
  }
  for(int i = x; i >= 1; i--){
    if(chk[i]){
      cout << i << endl;
      return 0;
    }
  }
  return 0;
}