A loop invariant is a condition that is guaranteed to be true at a given point within the body of a loop on every iteration. Loop invariants play a major role in axiomatic semantics, a formal reasoning system used to prove properties of programs. In a less formal way, programmers who identify (and write down!) the invariants for their loops are more likely to write correct code. Show the loop invariant(s) for your solution to the preceding exercise. (Hint: You will find the distinction between
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