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;

namespace CSharpSample01
{


    class Program
    {

        static bool Prime(int n)
        {
            int p = n;
            var list = new List<int>();
            for(int i = 2; i <= Math.Sqrt(p); i++)
            {
                //Console.WriteLine(i + "で割れるか");
                while(n % i == 0)
                {
                    list.Add(i);
                    n /= i;
                }  
            }

            if (n != 1) list.Add(n);

            //Console.Write(p + "：");
            //Console.WriteLine(string.Join(" ", list));

            if (list.Count == 1) return false;

            int a = list.First();
            foreach(var s in list)
            {
                if (s != a) return false;
            }

            return true;
        }


        static void Main(string[] args)
        {

            int X = int.Parse(Console.ReadLine());

            for (int i = X; i >= 2; i--)
            {
                if (Prime(i))
                {
                    Console.WriteLine(i);
                    return;
                }
            }

            Console.WriteLine(1);

        }
    }
}