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: Wrong Answer)

program exp
	implicit none
	integer :: y, c, i
	real(8) :: x

	read(*,*) x
	
    c = 1
	do i = 1, int(sqrt(x)) + 1
		do y = 2, int(log(x)/log(2.0_8))+1
			if (i**y <= x) then
				c = i ** y
			else
				exit
			end if
		end do
	end do
	
	write(*,'(i0)') c

end program exp