We define a mountain range via its peaks and valleys. Let (x1, y1), (x2, y2), ... (xn, yn) be a sequence of points in the upper half-plane satisfying the following conditions:
  1. (x1, y1) = (a,0) and (xn, yn) = (b,0)
  2. xi < xi+1 for i = 1 to n-1
  3. if yi-1 < yi then yi > yi+1 for i = 2 to n-1; conversely, if yi-1 > yi then yi < yi+1
Then, we call the set of line segments formed by joining the points (xi, yi) and (xi+1, yi+1) for i = 1 to n-1 a "mountain range".


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