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)

var main = function(input) {
  var X = parseInt(input);
  var max = X;
  var I;
  for(var b=X;0<b;b--){
    for(var p=2;p<100;p++){
    I = Math.pow(b,p);
      if(I === max){
        console.log(max);
      	return;
		} else if(max < I){
          break;
        } else if(max === 1){
          console.log('1');
        } else {
          max--;
        }           
    }
  }
  return　 0;
}

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