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 PYTHON3):

Solution:
import math
N=int(input())

for h in range(1,3501):
    for n in range(1,3501):
        x,y=N*h*n,4*h*n-n*N-h*N
        if y==0:
            continue
        w=x/y
        if w>0 and math.floor(w)==math.ceil(w):
            print(h,n,math.floor(w))
            exit()