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: Time Limit Exceeded)

using System;
using System.Web;
using System.IO;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Linq;
using System.Numerics;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Runtime.CompilerServices;
using static System.Math;

class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int max = 0;
        for (int i = 1; i <= n; i++)
        {
            int a = 1;
            while (true)
            {
                if (a * i > n) break;
                a *= i;
            }
            max = Max(max, a);
        }
        Console.WriteLine(max);
    }
}