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: Runtime Error)

import math

X = int(input())

if X == 1:
    print(1)
    exit()

for i in reversed(range(1, X+1)):
    for j in range(2, int(math.sqrt(i))+1):
        if math.isclose(math.log(i, j), round(math.log(i, j)), rel_tol = 0.0000001):
            print(i)
            exit()
    if i == 1:
        print(1)