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;
using static System.Console;

class Program {
	static void Main() {
		var X = int.Parse(ReadLine());
		var ans = 1;

		for (var b = 2; b * b <= X; b++) {
			for (var p = 2; ; p++) {
				if (Math.Pow(b, p) > X) {
					break;
				}
				ans = Math.Max(ans, (int)Math.Pow(b, p));
			}
		}
		WriteLine(ans);
	}
}