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 Lua (5.3.2) (judge verdict: Accepted)

X=io.read("n")
res=0
if X<4 then 
	res=1
else
	k=math.floor(math.sqrt(X))
	for i=2,k do
		local j=2
		while math.pow(i,j)<=X do
			j=j+1		
		end
		j=j-1
		res=math.floor(math.max(res,math.pow(i,j)))
	end
end
print(res)