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;

namespace abc097_b
{
    class Program
    {
        static bool calc(int n)
        {
            int x = 2;
            while (n % x != 0 && x <= Math.Sqrt(n)) x++;
            while (n % x == 0) n /= x;
            return n == 1;
        }
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            while (!calc(n)) n--;
            Console.WriteLine(n);
        }
    }
}