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 <bits/stdc++.h>
#define rep(i,n) for (int i=0; i<(n); ++i)
using namespace std;
using ll=long long;
int main(){
    double N;
    cin>>N;
    for(double h=1; h<=3500; ++h){
        for(double n=1; n<=3500; ++n){
            double w=(N*n*h)/(4*h*n-N*n-N*h);
            ll x=w;
            if(x==w&&w>0){cout<<h<<" "<<n<<" "<<(ll)w<<endl; return 0;}
        }
    }
}