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;

namespace ABC97_B
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var AA = (int)Math.Sqrt(N);
            AA *= AA;

            var max = 0;

            for (int i = N; i > AA; i--)
            {
                if (Checkn(i))
                {
                    max = i;
                    break;
                }
            }
            Console.WriteLine(AA < max ? max : AA);
        }


        public static bool Checkn(int n)
        {
            int i = 2;
            int tmp = n;
            List<int> listn = new List<int>();
            var factor = 0;

            while (i * i <= n)
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    listn.Add(i);
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) listn.Add(tmp);
            if (listn.Count == 1)
            {
                return false;
            }

            foreach (var a in listn)
            {
                if (factor == 0)
                {
                    factor = a;
                    continue;
                }
                else if (factor != a)
                {
                    return false;
                    
                }
            }
            return true;
        }

    }
}