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 <iostream>

using namespace std;

int main()
{
    long long N;
    cin>>N;

    for (long long h=1; h<=3500; h++)
    for (long long n=1; n<=3500; n++)
    {
        long long w = (long long)(1. / (4./N - 1./h - 1./n) + .5);
        if (4*h*n*w == N*n*w + N*h*w + N*h*n)
        {
            cout<<h<<" "<<n<<" "<<w<<endl;
            return 0;
        }
    }
}