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: Wrong Answer)

N = int(input())
import math
n = math.floor(N**0.5)
P = []
for i in range(2,n+1):
    J = 1
    for j in range(len(P)):
        if i % P[j] == 0:
            J = 0
            break
    if J == 1:
        P.append(i)
A = [1]
for i in range(len(P)):
    p = P[i]
    j = 1
    while p**j <= N :
        A.append(p**j)
        j += 1
ans = max(A)
print(ans)