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)

num = gets.chomp.to_i
i = 1
remenber = 0

loop do

    if i > 100
        puts remenber
        exit
    end

    j = 1

    # n乗の探索
    loop do
        #puts i**j

        if i**j > 1000
            break
        end

        if (i**j <= num) && ((i+1) ** j > num)
            if remenber < i ** j
                remenber = i ** j
            end
            break
        end

        j += 1
    end
 
    i += 1
end