Let $\left[\begin{array}{ccc}l_{11} & 0 & 0 \\ l_{21} & l_{22} & 0 \\ l_{31} & l_{32} & -10\end{array}\right]\left[\begin{array}{ccc}1 & u_{12} & u_{13} \\ 0 & 1 & u_{23} \\ 0 & 0 & 1\end{array}\right]$ be the $L U$ decomposition of the matrix $A=\left[\begin{array}{rrr}1 & 1 & 1 \\ 4 & 3 & -1 \\ 3 & 5 & a\end{array}\right]$. Then, the value of $a$ (in integer) is $\_\_\_\_$
