Staying fit is important for every superhero, and Spiderman is no exception. Every day he undertakes a climbing exercise in which he climbs a certain height of a tall building, rests for a minute, then climbs again, rests again, and so on. The exercise is described by a sequence of heights d1, d2, d3, ... , dm telling how many meters he is to climb before the first break, before the second break, and so on. From an exercise perspective it does not really matter if he climbs up or down at the ith climbing stage, but it is practical that sometimes climbs up and sometimes climbs down, so that he both starts and finishes at street level. Obviously, he can never be below street level! Also, he would like to climb as short a building as possible (he does not like to admit it, but he is actually afraid of heights). The building must be at least 2 meters higher than the highest point his feet reach during the workout.
He wants your help in determining when he should go up and when he should go down. The answer must be legal: it must start and end at street level (0 meters above ground) and it may never go below street level. Among the legal solutions he wants one that minimizes the required building height. When looking for a solution, you may not reorder distances.
If the distances are 20 20 20 20, he can either climb up, up, down, down or up, down, up, down. Both are legal, but the second one is better (in fact optimal) because it only requires a building of height 22, whereas the first one requires a building of height 42. If the distances are 3 2 5 3 1 2, an optimal legal solution is to go up, up, down, up, down, down. Note that for some distance sequences there is no legal solution at all (e.g., for 3 4 2 1 6 4 5).