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 v5.12) (judge verdict: Wrong Answer)

// コードをここに挿入。
function main(input) {
    const x = parseInt(input, 10);
    var max_b = Math.floor(Math.sqrt(x));
    var ans = 0;
    if (x === 1) {
        console.log(x);
    }
  else{
    for (var i = max_b; i > 2; i--) {
        var bp = i;
        while (bp < x) {
            bp *= i;
            if (bp < x && bp >= ans) {
                ans = bp;
            }
        }
    }
    console.log(ans);
  }
}

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