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: Wrong Answer)

X = int(input())
nums = set([1])
for i in range(2, int(1000 ** .5) +1):
    b = 2
    while True:
        temp = i ** b
        if temp > 1000:
            break
        nums.add(temp)
        b += 1
sorted_nums = sorted(list(nums), reverse=True)
# print(f"nums:{sorted_nums}", file=sys.stderr)
for i in range(len(sorted_nums) - 1):
    if sorted_nums[i] > X >= sorted_nums[i + 1]:
        print(sorted_nums[i + 1])