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.Linq;
using System.Collections.Generic;
using System.IO;

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(Console.ReadLine());
        }

        public static long[] Reads()
        {
            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }


        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var x = Read();
            var list = new List<long>();
            list.Add(1);
            for (int i = 1; i<=x ; i++)
            {
                for (int j = 2; j*j <=i ; j++)
                {
                    var tmp = i;
                    while (tmp > 1 && tmp % j == 0)
                    {
                        tmp /= j;
                    }
                    if (tmp == 1)
                        list.Add(i);
                }
            }
            Console.WriteLine(list.Max());



 
           
            Console.Out.Flush();
        }
    }
}