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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<math.h>
#include<algorithm>
using namespace std;

int main() {
	int x;
	cin >> x;
	double num = 0, old;
	double ans = 0;
	for (int b = 1; b <= x; b++) {
		for (int p = 2; p <= x; p++) {
			old = num;
			num = pow(b, p);
			if (num > x) {
				num = old;
				break;
			}
		}
		ans = max(num, ans);
	}
	cout << ans << endl;
	return 0;
}