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())
b = 1
ans = 0
while(1):
    b += 1
    p = 1
    if (b**2) > X:
        break
    while(1):
        p += 1
        if X < (b**(p+1)) and (b**p) <= X:
            ans = max(ans,b**p)
            break
if X==1:
    print(1)
    exit()
if X==2 or X == 3:
    print(1)
    exit()

print(ans)