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
$x=trim(fgets(STDIN));
$ans=1;
$i=floor(sqrt($x));
while($i>1){
$n=1;
while(pow($i,$n)<=$x){
$p=pow($i,$n);
++$n;
}
$ans=max($ans,$p);
--$i;
}
echo $ans;