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

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