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())

expotential_set = set()
for i in range(1, 1000):
    for j in range(2, 10):
        expotential_set.add(pow(i, j))

expotential_list = sorted(list(expotential_set))

distance = 10000000000000
for num in expotential_list:
    if num <= x and abs(num - x) < distance:
        distance = abs(num - x)
        ans = num

print(ans)