Consider the following function foo.$($a$)$ write a loop invariant $($LI$1)$ using just the variable $1,$ that remains true throughout the execution of the loop.$($b$)$ write a loop invariant $($LI$2)$ using variables x and i$,$ that remains true throughout the execution of the loop.$($c$)$ Prove that LI$2$ is indeed a loop invariant. You need to show that LI$2$ is true initially, and as soon as it enters the loop and at the end of each iteration of the loop.