City S is a one-dimensional city, and its coordinate system is identical to the number line. There are $n$ key points located at $x_1, \dots, x_n$. Any position at a distance $< r$ from any key point is forbidden (positions at distance $= r$ are allowed). Little Q is initially at coordinate $A$ in City S. He can perform the following actions:
- Walk from $x$ to $y$, which consumes $|x-y|$ time. This operation requires passing through all real-numbered points between $x$ and $y$, so it must be guaranteed that there are no forbidden points in the interval between $x$ and $y$.
- Jump from $x$ to $x+2R$, which consumes $\pi \cdot R$ time. This operation only requires that $x$ and $x+2R$ are allowed positions.
- Jump from $x$ to $x-2R$, which consumes $\pi \cdot R$ time. This operation only requires that $x$ and $x-2R$ are allowed positions.
Given $n, r, R, A, B$, and $x_1, \dots, x_n$, find the minimum time for Little Q to reach $B$. If it is impossible to reach $B$, output $-1$. It is guaranteed that $A$ and $B$ are both allowed positions.
This problem allows a relative error of $10^{-6}$. If your output is $p$ and the true answer is $q$, your answer is considered correct if $\dfrac{|p-q|}{\max(1,|q|)} \le 10^{-6}$.
Input
The first line contains five integers $n, r, R, A, B$.
The second line contains $n$ integers $x_1, \dots, x_n$.
Output
A single real number representing the answer.
Examples
Input 1
5 2 5 3 9 13 0 17 7 18
Output 1
55.1238898038
Constraints
For $100\%$ of the data, $1 \le n \le 500$, $1 \le r \le R \le 10^6$, $-10^9 \le A \le B, x_i \le 10^9$.
- Subtask 1 ($30\%$): $-10^5 \le r, R, A, B, x_i \le 10^5$.
- Subtask 2 ($30\%$): $n \le 50$.
- Subtask 3 ($40\%$): No special restrictions.