Suppose we have an n×n two-dimensional array A that we want to use to store integers, but we don’t want to spend the O(n²) work to initialize it to all 0’s, because we already know that we are only going to use up to n of these cells in our algorithm, which itself runs in O(n) time (not counting the time to initialize A). Show how to use an array-based stack S storing (i, j,k) integer triples to allow us to use the array A without initializing it and still implement our algorithm in O(n) time, even though the initial values in the cells of A might be total garbage.