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;
const int N=3500;
typedef long long LL;
LL n;
int main()
{
    cin>>n;
    for(LL x=1;x<=N;x++){
        for(LL y=1;y<=N;y++){
            LL d=4*x*y-n*(x+y);
            if(d>0 && (n*x*y)%d==0){
                printf("%I64d %I64d %I64d",x,y,(n*x*y)/d);
                return 0;
            }
        }
    }
    return 0;
}