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)

#coding: utf-8
import math

x = int(input())

maxcount = int(math.sqrt(x))

result = 0
for i in range(1,maxcount):
    j = 0
    while True:
        tmp = i ** (maxcount - j)
        j += 1
        if tmp > x:
            continue
        else:
            break
    print(tmp)
    if tmp > result and tmp <= x:
        result = tmp

print(result)