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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class MainClass
{
	public const long Giri = 1000000007;

	
	public static void Main(string[] args)
	{
		int x = int.Parse(Console.ReadLine());
		int n = 0;
		int max = -1;
		for(int k = 1; k < x; k++)
		{
			for(int j = 2; j < x; j++)
			{
				n = (int)Math.Pow(k,j);
				if(n<=x)
				{
					max=n;
				}
				if(n==x)
				{
					Console.WriteLine(x);
					return;
				}
				if(n>x)
					break;
			}
		}
		Console.WriteLine(max);
	}
	
	public static long GCD(long a, long b)
	{
		if(b == 1)
			return a;
		long p = b / a;
		return GCD(a, b - a*p);
	}
	
	public static string[] Input()
	{
		return Console.ReadLine().Split(' ');
	}

	
	public static int Clamp(int val, int max, int min = 0)
	{
		return Math.Min(max, Math.Max(min, val));
	}

}