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())

flag = False
for x in range(X):
    for i in range(2, X-x+1):
        n = X - x
        m = 0
        while True:
            if m == 0:
                m = i
            if n % i == 0:
                n = n / i
                if n == 1 and m != X - x:
                    flag = True
                if flag:
                    break
            else:
                break
        if flag:
            break
    if flag:
        break
if flag:
    print(X - x)
else:
    print(1)