Jumping Path

Popeye the Sailor loves to eat spinach. He also loves to smoke his corn-made pipe, and he smokes it constantly.

Popeye lives in the village of Sweethaven. The main street of Sweethaven is a straight line with $n$ public places, located at coordinates $x_1, x_2, \cdots, x_n$ on that line.

Popeye needs to get from point $A$ on the main street to point $B$. The Sweethaven authority has passed a law: smoking closer than $r$ to a public place is prohibited. Popeye has a pole of length $R \ge r$, so he can jump over the forbidden zones.

Popeye starts at point $A$. He can walk from $x$ to $y$ in $|x-y|$ time. At any time, he can use the pole to move from $x$ to $x+2R$ or $x-2R$ along a semicircle of radius $R$, which takes $\pi R$ time. At the end, Popeye must be at point $B$, and no point on his trajectory can be closer than $r$ to any public place.

The first line contains five integers $n$, $r$, $R$, $A$, and $B$ ($1 \le n \le 500$, $1 \le r \le R \le 10^6$, $-10^9 \le A, B \le 10^9$). The second line contains $n$ integers $x_1, x_2, \cdots, x_n$ ($-10^9 \le x_i \le 10^9$). All $x_i$ are pairwise distinct. Points $A$ and $B$ are different, and neither lies in a forbidden zone.

Print one real number, the smallest time. The answer is accepted if its absolute or relative error is at most $10^{-6}$. If it is impossible to get from $A$ to $B$, print $-1$.

In the example from the statement, one of the optimal trajectories is shown below. The elapsed time is $8 + 15\pi$.