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;
typedef long long ll;
int n;
int main(){
    scanf("%d",&n);
    for(int i=1;i<=3500;i++){
        for(int j=1;j<=3500;j++){
            ll x=1ll*n*i*j,y=4*i*j-1ll*n*j-1ll*n*i;
            if(y&&x%y==0&&x/y>=1){
                printf("%d %d %lld\n",i,j,x/y);
                return 0;
            }
        }
    }
}