Vasily lives along a long avenue. A bus runs along the avenue in a straight line. From the metro to Vasily's house
N bus stops. We will assume that the metro is located at the zero stop, at the point with coordinate 0.
Coming out of the metro, Vasily is in a hurry to go home, but Vasily does not like to wait for the bus at the bus stop. Since Vasily never waits for a bus, having approached the stop and not seeing the bus, he goes further along the avenue. In the event that Vasily notices the bus, he either returns to the stop or continues on his way to the next stop.
Vasily walks at a speed
U, the bus travels at a speed
V. Find the minimum distance
L that must be seen before the zero stop, so that he can walk at his own speed towards the house without fear that the bus will overtake him between stops.
Input
The first line of the input contains three numbers
N,
U and
V (N <= 1000, ;U and V – positive real numbers), the second line contains
N real numbers –
X1,
X2,...
Xn (0 < X1 < X2 <…<Xn <10
6), separated by spaces.
Imprint
In the output file, your program should output the number
L with an accuracy of 10
-4.
Examples
| # |
Input |
Output |
| 1 |
1 1 10
2
|
9.0000
|
| 2 |
5 1 10
1 2 4 8 16
|
28.0000
|