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;

class Program {
  static void Main() {
    int x = int.Parse(Console.ReadLine());
    int ans = 1;
    for (int b = 2; b * b <= x; b++) {
      for (int p = 2; ; p++) {
        int t = (int)Math.Pow(b, p);
        if (t <= x) ans = Math.Max(ans, t);
        else break;
      }
    }
    Console.WriteLine(ans);
  }
}