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 <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N=1e2+10;


int main(){
    ll n;
    cin>>n;
    for(ll i=1;i<=3500;i++)
        for(ll j=1;j<=3500;j++){
            ll rem=4*i*j-n*j-n*i;
            if (rem<=0) continue;
            if (n*i*j%rem==0){
                cout<<i<<" "<<j<<" "<<(n*i*j/rem);
                return 0;
            }
        }
}
