$($b$)$ The lattice filter shown below is folded with a factor $N=8$ and the folding sets are $S_A=\{A_1,A_4,A_7,A_2,A_3,A_5,A_8,A_6\},S_M=\{M_4,M_1,M_5,,,M_2,M_3,\}.$ Assume that the adder and the multiplier are pipelined by $1$ and $2$ latches respectively. Perform cutset retiming for folding so that all folded edges contain non$-$negative delays.