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 CPP):

Solution:
#include <stdio.h>
int n;

int main()
{
    scanf("%d",&n);
    //printf("y");
    for (long long i=1;i<=3500;i++)
    for (long long j=i;j<=3500;j++)
    {
        //printf("%lld %lld %lld\n",i,j,(i*j*n)  );
        if ( (3*i*j>n*(i+j) ) && (i*j*n)%( 4*i*j-n*(i+j) )==0  )
        {
            printf("%lld %lld %lld\n",i,j,(i*j*n)/(4*i*j-n*(i+j) ) );
            return 0;
        }

    }
}