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.

Examples

Input

10


Output

9


Input

1


Output

1


Input

999


Output

961
import math
num = int(raw_input())
num_max = 1
root_num = int(math.sqrt(num)+1)
for i in range (2,root_num):
    count = i**2
    if count <= num:
        while True:
            if count > num:
                break
            else:
                count *= i
        count = count//i
    if count > num_max:
        num_max = count
print num_max