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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

class Main {
  public static void main(String args[]) {
    Scanner sc = new Scanner(System.in);

    double num;

    System.err.print("num: ");
    num = sc.nextDouble();

    double temporaryNum = 1;

    while (num >= temporaryNum) {
      for (int i = 1; Math.pow(i, 2) <= num; i++) {
        for (int n = 2; Math.pow(i, n) <= num; n++) {
          if (temporaryNum < Math.pow(i, n)) {
            temporaryNum = Math.pow(i, n);
          }
        }
      }
    }
    System.out.println(temporaryNum);
  }
}