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In order to finally settle their long-running dispute over who is the faster cow, Bessie and her friend Elsie decide to hold a race across the farm.
The two cows start at the same location and begin running in the same direction at the same time. The progress of each cow is described by a series of "segments", during each of which the cow runs at a constant speed. For example, Bessie might run at a speed of 5 for 3 units of time, then at a speed of 10 for 6 units of time. Bessie and Elsie both run for the same total amount of time.
The cows would like your help in counting the number of leadership changes during their race. A leadership change happens at a point in time when cow A pulls into the lead of cow B, whereas the last time one cow was in the lead, it was cow B. For example, if B is in the lead and then A pulls ahead, then this is a leadership change. If B is in the lead, and then A becomes even with B for some time and then finally pulls ahead, then this also counts as a leadership change.
4 3 1 2 4 1 1 1 2 10 2 3 1 2 3 9
Bessie runs at a speed of 1 for 2 units of time, then at a speed of 4 for 1 unit of time, then at a speed of 1 for 1 unit of time, and finally at a speed of 2 for 10 units of time. Elsie runs at a speed of 2 for 3 units of time, then at a speed of 1 for 2 units of time, then finally at a speed of 3 for 9 units of time. Note that both cows run for a total of 14 units of time.
Elsie is ahead until time t=3, when both cows meet after both have traveled 6 units of total distance and travel together for 1 unit of time. Bessie then pulls ahead briefly (the first leadership change), only to be overtaken shortly thereafter by Elsie (the second leadership change). Elsie ends the race in the lead.