A city skyline is specified by $$$n$$$ integers $$$d_1, d_2, \ldots, d_n$$$ ($$$0 \lt d_1 \lt d_2 \lt \ldots \lt d_n$$$) and $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$.

A skyline surface consists of $$$n$$$ horizontal line segments, the $$$i$$$-th segment connects points $$$(d_{i-1}, h_i)$$$ and $$$(d_i, h_i)$$$, where $$$d_0 = 0$$$. Each segment is a roof of a building.

A cat (which is so small that can be considered a point) wants to get from the leftmost point of the skyline, $$$(0, h_1)$$$, to the rightmost point of the skyline, $$$(d_n, h_n)$$$. To achieve that, the cat performs a sequence of moves. Each move is one of two types:

1. Walk from point $$$(x_1, y_1)$$$ to point $$$(x_2, y_2)$$$. Both points must belong to the same surface segment, i. e. there exists $$$i$$$ such that $$$y_1 = y_2 = h_i$$$ and $$$d_{i-1} \le x_1, x_2 \le d_i$$$. A trajectory of a walk is a straight line segment.
2. Jump from point $$$(x_1, y_1)$$$ to point $$$(x_2, y_2)$$$. Points $$$(x_1, y_1)$$$ and $$$(x_2, y_2)$$$ must belong to different surface segments. A trajectory of a jump is a straight line segment and must satisfy the following constraints:
   • the distance between $$$(x_1, y_1)$$$ and $$$(x_2, y_2)$$$ is at most $$$L$$$;
   • the line segment between $$$(x_1, y_1)$$$ and $$$(x_2, y_2)$$$ does not intersect any of the buildings, i. e. there is no point $$$(x, y)$$$ belonging to the segment and integer $$$i$$$ such that $$$d_{i-1} \lt x \lt d_i$$$ and $$$y \lt h_i$$$.

The length of the cat's trajectory is the sum of lengths of all the moves in it. Find the shortest trajectory for the cat to get from $$$(0, h_1)$$$ to $$$(d_n, h_n)$$$, or determine that the goal is unreachable.