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: Runtime Error)

X = int(input())

if X < 4:
  print(1)
  exit(1)

p = 1
b = 2
m = 1
while 1:
  if b ** 2 > X: break
  
  cand = b ** p
  if cand > X:
    b += 1
    p = 1
    continue

  if cand > m:
    m = cand

  p += 1

print(m)