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)

require 'prime'
 
num = gets.chomp.to_i
 
i = 0
loop do
 
    # print Prime.take(i).last.to_i ** 2," ",Prime.take(i+1).last.to_i ** 2,"\n"
 
    if (Prime.take(i).last.to_i ** 2 <= num) && (Prime.take(i+1).last.to_i ** 2 > num)
        puts Prime.take(i).last.to_i ** 2
        break
    end
 
    i += 1
end