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 <stdio.h>
#include <math.h>

int solve(int n){
  for(int i=2; i<=sqrt(n); i++)
    if(n%i == 0){
      int ncopy = n;
      while(ncopy%i == 0)  ncopy /= i;
      if(ncopy == 1)  return 1;
    }
  return 0;
}

int main(){
  int n;  scanf("%d", &n);
  int ans = 1;
  for(int i=n; i>=1; i--)
    if(solve(i)){
      ans = i;
      break;
    }
  printf("%d\n", ans);
  return 0;
}