$(20$ points$)$ Execute the dynamic programming algorithm to find the optimal sequence in performing the multiplication $M_1{M}_2{M}_3{M}_4$ where the dimensions of the $4$ matrices are, respectively, $802,260,6020,2010,$ i$.$e$.r_0,r_1,r_2,r_3,r_4=80,2,60,20,10.$ Compute the $m_{ij}\text{'}$s in the table below. What is the optimal order of multiplication?

$\backslash$table$[[m_{11}=0,m_{22}=0,m_{33}=0,m_{44}=0$