Rain#2929
At the Meteorological Research Institute, researchers decided to study the formation of water bodies on various types of terrain during rainfall. To simplify the complexity of real-world scenarios, they constructed a two-dimensional model, where the terrain is described only by its height and length. In this model, the terrain is represented as an -segment broken line with vertices (x_0, y_0), \dots, (x_N, y_N), where x_0 < x_1 < \dots < x_N and y_i \neq y_j for all i < j. On the left at point x_0 and on the right at point x_N, the terrain is bounded by vertical mountains of great height. If the terrain were flat, after rainfall, the entire area would be covered by a water layer of depth . However, since the terrain is a broken line, the water flows and accumulates in depressions, forming water bodies.
You are required to determine the maximum depth among the water bodies formed after the rain.
The first line contains a natural number (1 \leq N \leq 100) and , a real number given with three digits after the decimal point (0 \leq H \leq 10^9). The next N+1 lines contain two integers x_i, y_i (-10000 \leq x_i, y_i \leq 10000, 0 \leq i \leq N).
Numbers in each line are separated by spaces.
Output a single number — the maximum depth found, accurate to decimal places.
Example 1