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: Accepted)

require 'prime'

X = gets.to_i

max = 1

for i in 2..X do
  ary = Prime.prime_division(i)

  if ary.all? {|i| i[1] == ary[0][1] && i[1] >= 2} then
    tmp = 1
    ary.map { |e|
      tmp *= e[0]**e[1]
    }
    max = [max, tmp].max
  end
  
end

p max