Is the following Doubly Non-negative matrix Completely Positive:

$\frac{1}{6}\begin{bmatrix} 2 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 \\0 & 2 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 0 & 2 & 1 & 1 & 0 & 1 & 1 & 0 \\0 & 1 & 1 & 2 & 0 & 0 & 0 & 1 & 1 \\1 & 0 & 1 & 0 & 2 & 0 & 1 & 0 & 1 \\1 & 1 & 0 & 0 & 0 & 2 & 1 & 1 & 0 \\0 & 1 & 1 & 0 & 1 & 1 & 2 & 0 & 0\\1 & 0 & 1 & 1 & 0 & 1 & 0 & 2 & 0\\1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 2\end{bmatrix}$