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;
class Program
{
    static void Main(string[] args)
    {
        int X = int.Parse(Console.ReadLine());
        for(int i = X; i >= 1; i--)
        {
            for(int j = 2; j < 32; j++)
            {
                int n = j * j;
                if (n > X) break;
                while (true)
                {
                    int n2 = n * j;
                    if (n2 <= X)
                        n *= j;
                    else
                        break;
                }
                if(n == i)
                {
                    Console.WriteLine(i);
                    return;
                }
            }
        }
        Console.WriteLine(1);
    }
}