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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
//var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
namespace AtCoderSolve
{
    class Solve
    {
        const int mod = 1000000007;
        static void Main(string[] args)
        {

            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);

            int X = int.Parse(Console.ReadLine());
            int ans = 0;
            for(var i = 1; i <= X; i++)
            {
                if (i == 1)
                {
                    ans = Math.Max(ans, i);
                    continue;
                }
                int k = i * i;
                while (k <= X)
                {
                    ans = Math.Max(ans, k);
                    k *= i;
                }

            }

            Console.WriteLine(ans);

            //Console.Out.Flush();
            
        }
    }



    public class Calculation
    {

    }

    public class Graph
    {

    }
}