# Problem R

Aspen Avenue

## Input

The input file starts with a positive even integer $N$ between $4$ and $2\, 000$ (inclusive), giving the total number of trees in the avenue. The next line contains two integers $L$ and $W$, where $1 \le L \le 10\, 000$ is the length of the road, in meters, and $1 \le W \le 20$ is the width of the road, in meters. The next $N$ lines each describe where Tim had dropped of the trees. Each such line contains an integer $0 \le p \le L$ indicating the position of a tree plant along the left side of the road, measured in meters from the start of the road.

## Output

Output the smallest total number of meters the tree plants need to be moved. The answer should be given with an absolute or relative error of at most $10^{-6}$.

Sample Input 1 | Sample Output 1 |
---|---|

4 10 1 1 0 10 10 |
2.4142135624 |

Sample Input 2 | Sample Output 2 |
---|---|

6 10 1 0 9 3 5 5 6 |
9.2853832858 |