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 Python (3.4.3) (judge verdict: Accepted)

X = int(input())

score =0
half_x = round(X/2)

answer = 0

if X < 3:
    print(1)

elif X <= 8:
    print(2)

else:
    while 1 < half_x:
        half_x -= 1
        
        for p in range(2, 10):
            
            score = pow(half_x,p)
            if score > X:
                continue
        
            if answer < score:
                answer = score
                
    print(answer)