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<int>(){
      (int)Math.Pow((int)Math.Pow(input, 1.0/2.0),2),
      (int)Math.Pow((int)Math.Pow(input, 1.0/3.0),3),
      (int)Math.Pow((int)Math.Pow(input, 1.0/5.0),5),
      (int)Math.Pow((int)Math.Pow(input, 1.0/7.0),7),
      (int)Math.Pow((int)Math.Pow(input, 1.0/9.0),9)
    };
    Console.WriteLine(list.Max());
  }
}