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>
#define rep(i,N) for(i=0;i<N;i++)

int main(){
  long n,x,i,j,prev;
  scanf("%ld",&n);
  int memo[n+1];
  rep(i,n+1) memo[i] = 0;
  memo[1] = 1;

  for(i=2;i<n+1;i++){
    x = i;
    while(1){
      if((x * i) < n){
        x *= i;
        memo[x] = 1;
      }
      else break;
      //printf("i=%d,x=%d\n",i,x);
    }
  }
  //printf("hi");
  for(i=n ; i >= 1; i--){
    if(memo[i] == 1){
    printf("%ld\n",i);
    break;
    }
  }

  return 0;
}