Consider the following code, assuming that $i,x,y,$ and $n$ are integers, with $n0.$

State a non$-$trivial loop invariant for variable $x.$

Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended.

Note: a correct proof of an incorrect invariant will still receive partial credit.

Give the final value of $x$ in terms of $n.$

Hint: is the pattern close to $($e$.$g$.$ off by one$)$ from some other pattern you might recognize?

Hint: you might need to include a condition for $y$ somewhere within your proof.

ilArr$0$;

xlArr$1$;

$//$ larr $($the invariant goes here$)$

while $in$ do

$//$

ylArrx$+2$;

$//$

xlArrx$**y$;

$//$

ilArri$+1$;

$//$

$//$

After the loop, $x=$