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 (7.3.0) (judge verdict: Runtime Error)

import math
x = int(input())
ans = (int(math.sqrt(X)))**2
for i in range(1,int(math.sqrt(x)+2)):
  for j in range(2,10):
    if i ** j <= x and i**j > ans:
      ans = i**j
    else:
      break
print(ans)