Let $A$ be a $4 \times 4$ matrix with reduced row echelon form given by $U = \begin{bmatrix} 1 & 0 & -1 & 1 \\ 0 & 1 & 3 & 2 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}$. Let the first two columns of $A$ be $\begin{bmatrix} 3 \\ 2 \\ -1 \\ 2 \end{bmatrix}$ and $\begin{bmatrix} 1 \\ 1 \\ -2 \\ 3 \end{bmatrix}$, and denote the third column of $A$ as $\begin{bmatrix} a \\ b \\ c \\ d \end{bmatrix}$. What is $\lfloor a+b+c+d \rfloor \% 5$? (% is the modulo operation. $\lfloor z \rfloor$ rounds $z$ to the smaller nearest integer.)