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: Runtime Error)

x = int(input())
p = 2
list_prob = []
ind = 0
i = 1
while p < 11:
    ind = i ** p
    while ind < 1001:
        list_prob.append(int(i ** p))
        i += 1
        ind = i ** p
    i = 1
    p += 1
list_prob.sort()
while i < len(list_prob):
    if list_prob[i] <= x and list_prob[i+1] > x:
        print(list_prob[i])
        break
    i += 1