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 AtCoder.ABC097
{
    class b
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Trim();
            var X = int.Parse(line);
            var list = new bool[1001];
            list[0] = true;
            list[1] = true;
            for(var b = 2; b < X; ++b)
            {
                var p = 2;
                while (Math.Pow(b, p) <= X)
                {
                    list[(int)Math.Pow(b, p)] = true;
                    ++p;
                }
            }
            for(var i = X; i >= 1; --i)
            {
                if (list[i])
                {
                    Console.WriteLine(i);
                    break;
                }
            }
        }
    }
}