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)

list = [1]
for i in range(2, 35):
	for j in range(2,12):
		k = i ** j
		if k < 1000 and not k in list:
			list.append(k)
		else:
			break
list.sort()
N = len(list)
K = int(input())
max = 1
for j in range(N):
	if K < list[j]:
		break
	else:
		max = list[j]
print(max)