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.Collections.Generic;
using System.Linq;
using static System.Console;

namespace ConsoleApp4
{
    class Program
    {
        private static int _x;

        static void Main()
        {
            _x = int.Parse(ReadLine());

            if (_x < 4)
            {
                WriteLine("1");
                return;
            }

            var a = Enumerable.Range(2, 30).Where(i => i * i <= _x);

            WriteLine(Hoge(a).Max());

        }

        private static IEnumerable<int> Hoge(IEnumerable<int> f)
        {
            return f.Select(variable => Enumerable.Range(1, 9).Select(e =>
            {
                var b = variable;

                while (1 < e)
                {
                    var c = b * variable;

                    if (_x < c)
                    {
                        break;
                    }

                    b = c;

                    e = e - 1;
                }

                return b;
            })
                .Max());
        }

    }
}