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: Wrong Answer)

x = int(input())

def prime_factorize(n:int):
    l = []
    if n == 1:
        l.append(1)
        return l

    while n % 2 == 0:
        l.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            l.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        l.append(n)
    return l

def judge (p:int):
    if p == 1:
        return True

    l = prime_factorize(p)
    if len(set(l)) == 1 and len(l) > 1:
        return True
    else:
        return False

for i in range(x,0,-1):
    if judge(i):
        print (i)
        exit ()