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: Accepted)

/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();//, b = sc.nextInt(), c=  sc.nextInt(), d = sc.nextInt();
		int sqrt = (int)Math.sqrt(a);
		List<Integer> list = new ArrayList<>();
		if(a<=3){
			System.out.println(1);return;	
		}
		for(int i=2;i<=sqrt;i++){
			for(int ii=2;;ii++){
				if(Math.pow(i,ii)<a){
					list.add((int)Math.pow(i,ii));
				} else if(Math.pow(i,ii)==a){
					list.add((int)Math.pow(i,ii));break;
				} else break;	
			}
		}
		Collections.sort(list);
		System.out.println(list.get(list.size()-1));
	}
}