“Phew, that was the last one!” exclaimed the garden
helper Tim as he threw the last tree plant to the ground. His
employer, countess Esmeralda Hunt who owned the estate, has
ordered him to arrange an avenue of aspen trees along both
sides of the front road leading up to the house. The first
trees in the avenue are supposed to be planted at the very
beginning of the road, and the last trees of the avenue at the
very end of the road. Tim, who was constantly being reminded of
her sense of accuracy, knew that the countess would insist on
the trees being placed in perfectly aligned tree pairs, one on
each side of the road, and with exactly the same spacing
between the pairs along the road. However, when bringing the
tree plants to the estate, Tim had just dropped them
arbitrarily along the left side of the road and was now facing
the task of moving the trees to their correct positions to meet
the countess’s requirements. Being stronger in mind than in
arms, and since it was time for a coffee break anyway before he
started digging, he sat down to figure out which trees to move
to which positions so as to minimize the total (Euclidean)
distance that he had to move the trees.
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
