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.Linq;
    using System;
    using System.Collections.Generic;
    class Program
    {
      static void Main(string[] args)
      {
        var input = int.Parse(Console.ReadLine());
        var list = new List<Double>(){
          Math.Pow(Math.Pow(input, 1.0/2.0),2),
          Math.Pow(Math.Pow(input, 1.0/3.0),3),
          Math.Pow(Math.Pow(input, 1.0/5.0),5),
          Math.Pow(Math.Pow(input, 1.0/7.0),7),
          Math.Pow(Math.Pow(input, 1.0/9.0),9)
        };
        Console.WriteLine(Math.Round(list.Max()));
      }
    }