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;
class Problem02{
	static void Main(string []args){
		string t=Console.ReadLine();
		int X=int.Parse(t);
		for(int i=X;i>=1;i--){
			if(beki(i)==true){
				Console.WriteLine(i);
				break;
			}
		}
	}
	static bool beki(int x){
			if(x==1) return true;
		for(int i=2;i<=x/2;i++){
			if(x%i!=0) continue;
			int n=x;
			for(int j=2;n>=0;j++){
				n /= i;
				if(n==1)return true;
				else if(n%i!=0)return false;
			}
		}
		return false;
	}
}