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 'set'; require 'prime'; require 'pp'
INF=Float::INFINITY; MOD=10**9+7
x = gets.chomp.to_i

if x == 1
  puts 1
  exit
end

ans = 0
2.upto(100).each do |i|
  cur = i * i
  next unless cur <= x
  while cur <= x
    cur *= i
  end
  cur /= i
  ans = cur if ans < cur
end

puts ans