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<cstdio>
long long gcd(long long a,long long b){return b?gcd(b,a%b):a;}
int main(){
	int n; scanf("%d",&n);
	for(int i=1;i<=3500;++i)
		for(int j=1;j<=3500;++j){
			long long up=4ll*i*j-n*i-n*j,down=1ll*n*i*j,gg=gcd(up,down);
			if(up*down<=0) continue;
			up/=gg; down/=gg;
			if(up==1){
				printf("%d %d %lld",i,j,down); return 0;
			}
		}
	return 0;
}