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

Four matrices M1, M2, M3 and M4 of dimensions p q, q r, r s and s t respectively can be multiplied in several ways with different number of total scalar multiplications. For example when multiplied as ((M1 M2) (M3 M4)), the total number of scalar multiplications is pqr + rst + prt. When multiplied as (((M1 M2) M3) M4), 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

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