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>
using namespace std;
using ll=long long;
ll N,h,n,w;
int main(){
  cin>>N;
  for(ll i=1;i<=3500;i++)
    for(ll j=1;j<=3500;j++)
      if(N*(i+j)<(4*i*j) && (N*i*j)%(4*i*j-N*(i+j))==0){
      h=i;n=j;w=(N*i*j)/(4*i*j-N*(i+j));
      }cout<<h<<" "<<n<<" "<<w<<endl;
  return 0;
}