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())
a=n*3//4+3
for i in range(max(n//4,1),a):
    for j in range(a-3,3501):
        k=4*i*j-n*(i+j)
        if k==0:
            continue
        x,y=divmod(n*i*j,4*i*j-n*(i+j))
        if y==0 and x>0:
            print(i,j,x)
            exit()