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<stdio.h>



using lint = long long;
int main() {
	lint N;
	scanf("%lld", &N);
	for (lint h = 1; h <= 3500; h++) {
		for (lint n = 1; n <= 3500; n++) {
			lint p = 4 * h*n;
			lint q = N*n;
			lint r = N*h;
			lint s = p - q - r;
			if (s > 0 && (N*h*n) % s == 0) {
				printf("%lld %lld %lld",h,n, N*h*n / s);
				return 0;
			}
		}
	}
}