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:
n=int(input())
for i in range(max(1,n//4),3501):
  for j in range(max(1,n//4+1),3501):
    if 4*i*j-i*n-j*n!=0:
      num1=i*j*n/(4*i*j-i*n-j*n)
      num2=i*j*n//(4*i*j-i*n-j*n)
      if num1==num2 and num1>0:
        print(i,j,num2)
        exit()