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

ps = [2]

(3..31).each do |n|
  if ps.all? {|p| n%p != 0}
    ps << n
  end
end

ns = [1]

ps.each do |b|
  p = 2
  while b**p <= 1024
    ns << b**p
    p += 1
  end
end

ns = ns.sort

(0..ns.length-1).each do |i|
  if x < ns[i]
    p ns[i-1]
    exit 0
  end
end