$4.(25$ points$)$ The following code segment is given:

i $<0$

$1$

While i $<$ n do

i i$+1$

$211$

$($a$)(15$ points$)$ Let n $>0,$ and assume n is odd. Provide a loop invariant, p$,$ for the following code. Include Eveni$)$ in your loop invariant, to help with part $($b$)$ below. Prove the correctness of the loop invariant specified above by showing that $($p $^$ B$)($S$\}$p is a good Hoare triple.