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 (gfortran v4.8.4) (judge verdict: Wrong Answer)

program exponential
  implicit none
  integer :: x, n, i, s, t, k
  read(*,*) x
  if (x.lt.4) then
    write(*,'(i0)') 1
  end if
  k = 1+int(sqrt(real(x,8)))
  s = 0
  do i = 2, k
    t = i*i
    do
      if (t.gt.x) exit
      if (s.lt.t) s = t
      t = t*i
    end do
  end do
  write(*,'(i0)') s
  stop
end program exponential