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 solve(num):
    a = num
    result = []
    x = []
    for i in range(2, int(num**(1/2))+1):
        if num%i==0:
            c = 0
            while num%i==0:
                num //= i
                c += 1
            result.append(c)
    if num!=1:
        result.append(1)
    return all(i%2==0 for i in result)

for i in range(x, 0, -1):
    if solve(i):
        print(i)
        break