Consider the following arithmetic expression: F $=($A$0+$ A$1+...+$ A$7)$ x $($B$0+$ B$1+...+$ B$7)7\mathrm{.}1$ Show a minimal height tree implementation of F assuming unlimited processors. Compute the speedup S$1$ and the efficiency E$1.7\mathrm{.}2$ Find a minimal height tree implementation of F assuming $4($four$)$ processors available, each being able to execute the addition or multiplication operation in one time step. Compute the speedup and efficiency, S$2$ and E$2,$ respectively. $7\mathrm{.}3$ Suppose you want to implement F using a $4$x$4$ mesh connected network. a$)$ Describe a procedure that implements F in minimal time on the mesh network. Also, find the speedup and efficiency of your parallel mesh implementation. b$)$ If your boundary processors are connected by end$-$around or wrap$-$around connections $($toroidal connections$),$ show how your solution improves in terms of the speedup and efficiency.