Statement

William is a huge fan of the Rollercoaster Typhoon videogame, and spends a great deal of his time designing rollercoaster tracks. However, William's wild imagination often clashes with the laws of physics that such a track has to comply with. A rollercoaster track is defined by a sequence H_i of N integer values, representing the height of the pillars upon which the track is laid, in the order in which they are connected by the tracks. If a contiguous subsequence of at least three of these values is in arithmetic progression (that is, the difference between consecutive values is positive and constant), the corresponding section of the track is automatically motorized. Whenever William tests his design, a test car drives through it from i=0 on, following these rules: (1) Whenever the car reaches the start of a motorized section, it is hooked by the lifter which drops it at the last pillar of the section, from which the car starts a free fall as in rule 2...