Problem: You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

* It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:


N


Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:


h n w

Examples

Input

2


Output

1 2 2


Input

3485


Output

872 1012974 1539173474040


Input

4664


Output

3498 3498 3498

Solution (in JAVA):

Solution:
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main{
	static IntStream REPS(int v){return IntStream.range(0,v);}
	static IntStream REPS(int l,int r){return IntStream.rangeClosed(l,r);}
	static IntStream INS(int n){return REPS(n).map(i->getInt());}
	static Scanner s=new Scanner(System.in);
	static int getInt(){return Integer.parseInt(s.next());}
	static long getLong(){return Long.parseLong(s.next());}

	public static void main(String[]$){
		long N=getLong();
		for(long h=0;h<=3500;++h) {
			for(long n=0;n<=3500;++n) {
				long Nhn=N*h*n;
				long v=4*h*n-N*n-N*h;
				if(v>0&&Nhn%v==0) {
					System.out.println(h+" "+n+" "+(Nhn/v));
					return;
				}
			}
		}
	}
}