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 <cmath>
#define ll long long int
using namespace std;

int main(int argc, char const* argv[])
{
	int x;
	cin >> x;
	if(x == 1){
			cout << 1 << endl;
			return 0;
	}
  	int max = 1;
	int y = 8;
	while(y < x)y = y * 2;
	if(y / 2 > max && y / 2 <= x)max = y /2;
	for(int i = 3; i < sqrt(x); i+=2){
			int z = i*i*i;
			while(z < x)z = z*i;
      		if(z /i > x)continue;
			if(z/i > max)max = z/i;
	}
	cout << max << endl;
	return 0;
}