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 sys
N=int(input())
if N%2==0:
  print(N//2,N,N)
  sys.exit()
for a in range(1,3501):
  for b in range(1,a):
    M=N*a*b
    L=4*a*b-N*(a+b)
    if L>0:
      if M%L==0:
        print(a,b,M//L)
        sys.exit()