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: Accepted)

<?php
$X = trim(fgets(STDIN));
$m = floor(sqrt($X));
$mm = 0;
for($i=2;$i<$m;$i++) {
  $j = 1;
  while (!(pow($i, $j) <= $X && $X < pow($i, $j + 1))){
    $j++;
  }
  $mm=max(pow($i,$j),$mm);
  //printf("%d*%d %d\n",$i,$j,$mm);
}
printf("%d\n",max($m*$m,$mm));