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: Accepted)

program exp
implicit none
integer i,j,base,index
integer in,temp
read *, in ! 1<=in<=1000
base = 1
index =1
do i=1,int(sqrt(real(in)))  ! Base of exponential
  do j=1, 9 ! Index of exponential, 2^10>1000 therefore j<=9
    if(i**j<=in) then
      if(i**j>base**index) then
        base=i
        index = j
      end if
    end if
  end do
end do
print *, base**index
end program exp