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.chomp.to_i
#p b
a = 0
b = []
for i in 1..100
  if (Math::log(i)).to_f <= (Math::log(X)).to_f
   for p in 2..10 
       if (p * Math::log(i)).to_f <= (Math::log(X)).to_f
         a = i ** p
       end
   end
   b.push(a)
 end
end
puts b.max