We want to multiply a sequence of matrices $M_1, \ldots, M_n$ with the minimum number of multiplications. Let $m_{i,j}$ be the minimum number of multiplications to multiply $M_i, \ldots, M_j$. We can derive a recursion of $m_{i,j}$, where $r_i$ and $c_i$ are the numbers of rows and columns of the matrix $M_i$ respectively.

$m_{i,j} = \min_{i \le k < j}\left(m_{i,k} + m_{k+1,j} + r_i c_k c_j\right)$

(1)

When we compute all $m_{i,j}$'s with Equation 1, we must follow an order of $i$ and $j$ so that the $m$'s on the right-hand side are all known when we compute $m_{i,j}$. Please select all the correct orders in the following choices.