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 PYTHON):

Solution:
# -*- coding: utf-8 -*-
N=input()

for a in range(1,3501):
    for b in range(1,3501):
        if (4*a*b-N*(b+a))!=0:   #Cの計算式の分母がゼロではない
            if (N*a*b)%(4*a*b-N*(b+a))==0: #Cの計算式
                c=(N*a*b)/(4*a*b-N*(b+a))
                if 0<c:
                    print a,b,c
                    quit()