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;

namespace _097b
{
    class Program
    {
        static void Main(string[] args)
        {
            int X = int.Parse(Console.ReadLine());
            int ans = 1;
            for(var i = 2; i*i <= X; i++){//2乗フィルタ
                for(var j = i*i; j <=X; j*=i){//2乗以上フィルタ
                    ans = Math.Max(ans,j);
                }
            }
            Console.WriteLine(ans);
        }
    }
}