Four Matrices \(M_1 , M_2, M_3\) and \(M_4\) of dimensions \(p \times q, \ q…

Four Matrices $M_1 , M_2, M_3$ and $M_4$ of dimensions $p \times q, \ q \times r , \ r \times s$ and $s \times t$ respectively can be multiplied in several ways with different number of total scalar multiplications. For example when multiplied as $((M_1 \times M_2) \times (M_3 \times M_4))$  the total number of scalar multiplications is $pqr + rst + prt$. When multiplied as $(((M_1 \times M_2) \times M_3) \times M_4)$, the total number of scalar multiplications is $pqr + prs + pst$.

If $p=10, q=100, r=20, s=5$ and $t=80$, then the minimum number of scalar multiplications needed is