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
max = 0
if x == 1
  puts 1
else
  for i in 2..(Math.sqrt(x))
    beki = 0
    j = 0
    while beki < x
      beki = i**j
      j += 1
    end
    beki = i**(j-2)
    if max < beki
      max = beki
    end
  end
  puts max
end