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)

x = gets.chomp.to_f
max = 1

for i in 2..31
  v = Math.log(x) / Math.log(i.to_f)
  value = v.round(10)
  if value >= 2.0
    new_num = i ** value.floor
    if new_num > max
      max = new_num
    end
  end
end

puts max