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 static System.Console;
using static System.Convert;

class Program
{
    static void Main(string[] args)
    {
        var max = ToInt32(ReadLine());
        for(var i = max; i > 0; i--)
        {
            var num = i;
            var fig = FigureBreak(i);
            while (num%fig==0)
            {
                if (fig == 1) break;
                num /= fig;
            }
            if (num == 1) { WriteLine(i);break; }
        }
    }

    private static int FigureBreak(int num)
    {
        var result = 1;
        for(var i = 2; i< num; i++)
        {
            if (num % i == 0) { result = i;break; }
        }
        return result;
    }
}