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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int main()
{
	int X;
	scanf("%d", &X);
	
	int p, x, y;
	for (x = X; x > 1; x--) {
		for (p = 2; p * p <= x; p++) {
			if (x % p == 0) {
				y = x;
				while (y % p == 0) y = y / p;
				if (y == 1) break;
			}
		}
		if (p * p > x) continue;
		else break;		
	}
	
	printf("%d\n", x);
	fflush(stdout);
	return 0;
}