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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

x = int(input())
li = [False] * (x + 1)
li[1] = True

for i in range(x):
    for j in range(2, x):
        if i ** j < x + 1:
            li[i ** j] = True

for i in reversed(range(x + 1)):
    if li[i]:
        print(i)
        break