$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$. $$\textbf{A} = \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \end{bmatrix} \\ \textbf{B} = \begin{bmatrix}b_1 & b_2 & b_3 & b_4 \end{bmatrix} \\ \textbf{C} = \begin{bmatrix} c_1 & c_2 & c_3 & c_4 \end{bmatrix} \\ \textbf{D} = \begin{bmatrix} d_1 & d_2 & d_3 & d_4 \end{bmatrix} $$

It is known that $\textbf{B}$ is not scalar multiple of $\textbf{A}$. Also, $\textbf{C}$ is linearly independent of $\textbf{A}$ and $\textbf{B}$. Further, $D=3 \textbf{A} + 2 \textbf{B} + \textbf{C}$.

The rank of the matrix $\begin{bmatrix} a_1 & a_2 & a_3 & a_4 \\ b_1 & b_2 & b_3 & b_4 \\ c_1 & c_2 & c_3 & c_4 \\ d_1 & d_2 & d_3 & d_4 \end{bmatrix}$ is __________