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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
//上から順番に数えていく。
fscanf(STDIN, "%d", $x);
//平方根
$rt = intval(sqrt($x));

if($x == 1){
	echo 1;
  	exit;
}

$answerMAX = 0;
$answer = 0;
//ルートまで回す。
for($b = 2; $b <= $rt; $b++){
    $p = 2;
  //基準値用意
  while(true){
    if(pow($b, $p) <= $x){
    $answer = pow($b, $p);
    $p++;
    }
    else break;
  }
  if($answerMAX < $answer){
    $answerMAX = $answer;
  }
}
echo $answerMAX;