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)

import math

X = int(input())
sqrtX = math.floor(math.sqrt(X))
ans1 = sqrtX * sqrtX

# 解候補
anslist = [2**3, 2**5, 2**7, 2**9, 3**3, 3**5, 3**7, 5**3, 6**3, 7**3, 10**3]
ans2 = 0
for num in anslist:
    if num <= X and num > ans1: ans2 = num

print(max(ans1,ans2))