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: Wrong Answer)

#include <stdio.h>
#include <math.h>

int max(double);

int main(void){
  int X, b, p;
  int ans = 0, temp;
  scanf("%d",&X);
  if(X < 4){
    ans = 1;
  }
  if(ans == 0){
    for(b = 2; b <= X; b++){
      p = max(log(X)/log(b));
      if(p == 1) break;
      temp = (int)pow(b, p);
      if(ans < temp) ans = temp;
    }
  }
  printf("%d\n", ans);
  return 0;
}

int max(double val){
  int i = 0;
  while(i <= val) i++;
  return (i - 1);
}