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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

program beki
  implicit none

  integer :: x, n, p, b

  read(*,*) x

  n = 1
  if (x < 4 ) then
     n = 1
  else
     do b = 2, x-1
        p = 2
        do while ( b**p <= x )
          
           if ( n < b**p ) then
              n = b**P
           end if
           p = p + 1
        end do
     end do
  end if
  write(*,*) n
     
  stop
end program beki