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 Ruby (2.7.1) (judge verdict: Accepted)

#prime_divisionを用いた。
require "prime"
x = gets.chomp.to_i
x.downto (1) do |i|
    ans = i.prime_division
    size = ans.size
    count = 0
    if size == 1 && ans[0][1] != 1 && x >= 4
        puts i
        break
    elsif size >= 2 
        count = 0
        me = ans[0][1] 
        ans.each do |i|
            if me == i[1] && me != 1 
                count += 1
            end
        end
        if count == size
            puts i
            break
        end
    elsif x < 4
        puts "1"
        break
    end
end