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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function main(input) {
  const x = parseInt(input.trim(), 10)

  let b = new Set([1])

  for (let j = 2; j <= 10; j++) {
    for (let i = 2; i ** j <= x; i++) {
      b.add(i ** j)
    }
  }

  console.log(Math.max(...b))
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'))