Consider the following function that is intended for a guessing game that attempt to guess a number between 1 and 100, that a user might have thought of. 1. Suppose you intend to maintain the following loop invariant: the number to be guessed is somewhere in the interval [lo, hi]. Is this invariant maintained in each iteration of the loop? Explain why or why not 3. Suppose we make two changes in the algorithm: first, initialize hi to 101 ; second, update lo to mid +1 if the user's value is bigger than mid. The modified code maintains a loop invariant that is stronger than the invariant described in part a. Describe the loop invariant in the modified code, and briefly explain your answer 4. Using your updated invariant, give an induction proof that the modified algorithm works correctly