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: Runtime Error)

x = gets.to_i

num = [1]
b = 2
p = 2

while true
  result = b ** p
  if b ** 2 > x
  ¦ break
  elsif result > x
  ¦ b += 1
  ¦ p = 2
  else
  ¦ num << result
  ¦ p += 1
  end
end

puts num.max