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: Accepted)

x = int(input())
def createC(x, z):
  tmp = []
  for y in range(x):
    p = pow(y+1, z)
    if p <= x:
      tmp.append(p)
    else:
      return tmp

z = 2
max_c = 1
while True:
  if x == 1:
    break
  c_tmp = createC(x, z)
  if len(c_tmp) != 1:
    s = sorted(c_tmp)
    if max_c < s[-1]:
      max_c = s[-1]
    z += 1
  else:
    break
print(max_c)