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: Wrong Answer)

from math import sqrt
X = int(input())

# 素因数分解して要素数が 1 であれば終了
def f():
    for ans in range(X, 0, -1):
        x = ans
        # print(x)
        div = 2
        if x < div: return 1
        while x % div != 0:
            div += 1
        ctr = 0
        # print(div)
        while x > 1:
            if x % div != 0: break
            x //= div
            ctr += 1
        if x == 1 and ctr > 1:
            return ans

print(f())