Triples

A cute quokka joined CPMSoc this year and while being part of CPMSoc, he learned that some triples are very interesting. More specifically, the set of triples $(x_i, y_i, z_i)$ that have the following properties:

$x_i + y_i + z_i = 20$ for all $i$,
$x_i \neq x_j$ for any $i, j$ where $i \neq j$,
$y_i \neq y_j$ for any $i, j$ where $i \neq j$,
$z_i \neq z_j$ for any $i, j$ where $i \neq j$,
And lastly, the numbers $x_i, y_i, z_i$ are all non-negative integers for all $i$, $(x_i, y_i, z_i \in \mathbb{Z}^{+} \cup {0})$.

To satiate his curiosity, he wants you to find the largest set of triples that satisfy the above properties. You can provide the $3k$ numbers separated by either an empty-space or a comma. Your numbers will be of the following form:

x_1, y_1, z_1
x_2, y_2, z_2
...
x_k, y_k, z_k

For all the tasks, including this one, you can submit as many times as you like with no penalty! Only your best submission will be counted.

Triples

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