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
#include<iostream>
using namespace std;
#define int long long
signed main()
{
    int a;cin>>a;
    int key=a/4+1;
    for(int i=key;i<3505;i++){
        for(int j=key;j<3505;j++){
            int e=(4*i*j)-(a*i)-(a*j);
            int m=a*i*j;
            if(e!=0&&m%e==0&&m/e>0){
                cout<<i<<" "<<j<<" "<<m/e<<endl;
                return 0;
            }
        }
    }
}