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 (2.3.3) (judge verdict: Wrong Answer)

x = gets.to_i

x.downto(1) do |i|
    2.upto(i) do |j|
        if i % j == 0
            y = i
            cnt = 0
            while y % j == 0
                y /= j
                cnt += 1
            end
            if y == 1 && cnt > 1
                puts i
                exit
            end
        end
    end
end