Describe and analyze a data structure to support the following operations on an array a[1 . . n] as quickly as possible. initially, a[i] = 0 for all i. • settoone(i) given an index i such that a[i] = 0, set a[i] to 1. • getvalue(i) given an index i, return a[i] • getclosestrightzero(i) given an index i, return the smallest index j ≥ i such that a[j] = 0, or report that no such index exists. the first two operations should run in worst-case constant time, and the amortized cost of the third operation should be as small as possible. 3