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)

# -*- coding:utf-8 -*-
import math

def solve(X):
	ans = X
	# b^p = ansとなるansを探す
	for b in range(2, X):
		p = math.log(ans, b) # 精度で死ぬ(log(100, 10)など)
		if float.is_integer(p):
			return ans
	return 1

def solve2(X):
	# 全探索
	for x in range(X, 1, -1):
		for p in range(2, x):
			for b in range(2, x):
				bp = b**p
				if bp == x:
					return x
				if bp >= x:
					break
	return 1

if __name__ == "__main__":
	X = int(input())
	print(solve2(X))