Let us extend the binary search algorithm in the following way: in each iteration split the remaining elements into three lists of equal sizes (more or less equal). Let the sub lists be given by indices [l..m], [m + 1..n 1], [n..r]. Now compare the key with the elements in positions (l, m),(m + 1, n 1) and (n, r) to determine which sub list the key belong to (if at all). Based on the result of the comparisons (6 in total) remove the elements in at least two sub lists from consideration. Describe this algorithm in pseudo-code and analyze the time complexity using the O() notation.