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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
  fscanf(STDIN, "%d", $N);
  $n = floor(sqrt($N));
  $ans = 0;
  for($i=2;$i<$n;$i++){
    $k = 1;
    while(!pow($i, $k) <= $N && $N < pow($i, $k + 1)){
      $k++;
    }
    $ans = max(pow($i, $k), $ans);
  }
  echo max($n*$n, $ans);
?>