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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func main() {
	var x int
	fmt.Scan(&x)
	for i := x; i >= 1; i-- {
		if isPow(i) {
			fmt.Println(i)
			break
		}
	}
}

func isPow(n int) bool {
	if n == 1 {
		return true
	}
	for i := 2; i <= n/2; i++ {
		pow := i * i
		for pow <= n {
			if pow == n {
				return true
			}
			pow *= i
		}
	}
	return false
}