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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var X = int.Parse(Console.ReadLine());

            var result = 1;
            for(var b = 2; b<=(int)Math.Sqrt(X); b++)
            {
                for (var p = 1; (int)Math.Pow(b, p) <= X; p++)
                {
                    var y = (int)Math.Pow(b, p);
                    if (y > result)
                    {
                        result = y;
                    }
                }
            }

            Console.WriteLine(result);
        }
    }
}