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: Wrong Answer)

package main

import (
        "fmt"
        "math"
)

func solution(x int) int {
        if x == 1 {
                return 1
        }
        b := int(math.Floor(math.Sqrt(float64(x))))
        tmp := 1
        out := -1 << 31
        for i := b; i > 1; i-- {
                for tmp <= x {
                        tmp *= b
                }
                tmp /= b
                out = max(out, tmp)
        }
        return out
}

func max(x, y int) int {
        if x > y {
                return x
        }
        return y
}

func main() {
        var x int
        fmt.Scan(&x)
        fmt.Println(solution(x))
}