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.to_i
arr = Array.new

ans = 1
b = 2
p = 2
while b <= Math.sqrt(X)
  n = b**p
  if n <= X
    ans = [ans, n].max
    arr += [n]
    p += 1
  else
    b += 1
    while arr.include?(b)
      b += 1
    end
    p = 2
  end
end

puts ans