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: Wrong Answer)

<?php
fscanf(STDIN, '%d', $x);
$b = 0; $p = 0;
$ret = 0;
for($p = 2; $b ** $p <= $x; ++$p) {
    for($b = 1; $b ** $p <= $x; ++$b) {
        $ret = $b ** $p;
//echo $b. "\n";
//echo $p. "\n";
//echo $ret. "\n";
//echo "\n";
    }
}
echo $ret. "\n";