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 Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
    val x = io.StdIn.readInt

    if (x == 1) println(1)
    else {

        /*
        def exponentiation(base: Int): Int = {
            var tmp = base
            while (tmp < x) tmp *= base

            if (tmp == x) x
            else tmp/base
        }
        */

        def exponentiation(base: Int, acc: Int): Int =
            if (x < acc) acc/base
            else exponentiation(base, acc*base)

        // 1 <= 基数 <= √x
        val result = (2 to math.sqrt(x).toInt).map(exponentiation(_, 1)).max
        println(result)

    }

}