A sequence is bitonic if it monotonically increases and then monotonically decreases, or if it can be circularly shifted to monotonically increase and then monotonically decrease. For example the sequences 1, 4, 6, 8, 3, -2, 9, 2, -4, -10, -5, and 1, 2, 3, 4 are bitonic, but 1, 3, 12, 4, 2, 10 is not bitonic. (See Chapter 27 for a discussion of bitonic sorters, and see Problem 15-1 for the bitonic Euclidean traveling-salesman problem.)