4. Let A = [a], 22, ..., an be an array of numbers. Let's define a 'reverse' as a pair of distinct indices i, j {1,2,...,n} such that i aj; i.e., di and a; are out of order. For example - In the array A = (1, 3, 5, 2, 4, 6), (3, 2), (5, 2) and (5, 4) are the only reverses i.e. the total number of reverses is 3. (d) Assume that the inner loop works correctly. Using a loop-invariant proof for the outer loop, formally prove that your pseudo-code correctly sorts the given array. Be sure that your loop invariant and proof covers the initialization, maintenance, and termination conditions