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 (Clang 3.8.0) (judge verdict: Accepted)

#include<stdio.h>

int main(void){

  int X;

  scanf("%d", &X);

  int b=0;
  int p=0;

  int ans=0, pow=0, dif=1000, buf=1000;

  if(X <= 3){
    printf("1\n");
    return 0;
  }

  for(b=2; b <= 31; b++){
    pow = b*b;

    for(p=2; pow <= X; p++){
      buf = X - pow;

      if(buf == 0){
        printf("%d\n", X);
        return 0;
      }else if(buf < dif){
        ans = pow;
        dif = buf;
      }

      pow = pow * b;
    }
  }

  printf("%d\n", ans);

  return 0;

}