\begin{problem}{Jogging}{jogging.in}{jogging.out}{2 seconds}

It's Sunday, November 1, 2390, and Eddy has just been elected 
to the World Council. Of course, it is a very interesting and responsible 
job, and Eddy is eager to work in the Council, but there is a problem:  
Eddy is keen on sport. In particular, he likes jogging and he has been jogging 
at least thirty minutes each day of his life since he was a little boy. 
Now Eddy will have even less free time than ever before, when he was just a 
teacher. How will he find spare time for jogging?

Eddy %has considered this question for a long time and finally 
decided that 
he would jog on his way to his work. Of course, the Council building is 
rather far away from his house, so he wants to combine jogging with 
travelling by public transport. Now it has to be told that 
the moving pathways are the only means of public transport in the Capital.
Each line of pathways consists of a pair of straight pathways running 
in opposite directions with the same speed $v_1>0$. These pathways are very 
long and relatively narrow, so for the purpose of this task they can 
be considered sharing an infinite straight line on the plane. Besides, for 
each pathway two numbers are given, $T^+_i$ and $T^-_i$ --- the time 
necessary for boarding and leaving this pathway.
Note that crossing a pathway doesn't take any additional time, but changing 
from the $i$-th pathway to the $j$-th in their intersection point (which in fact 
is not an intersection since there are special bridges built at these points) 
takes exactly $T^-_i+T^+_j$ seconds.

Of course, Eddy wants to jog also on the pathways, so he'll move along the 
pathways with the ground speed $v_1+v_2$ where $v_2>0$ is the speed of 
Eddy while jogging on still ground. 

Now he wants {\em you} %, a programmer from the World Council Programming Center, 
to find a route from his house to the Council building that would require 
as little time as possible. %(after all, he is very pressed with his new business). 
This route should consist of several segments, some of which can lie on 
one of the existing pathways. 
% The buildings are very sparse in the Capital, 
% so it is indeed possible to jog along a straight path in the city. 

\InputFile

The first line of input consists of a single integer $N$, $0\leq N\leq 50$ --- 
the number of pairs of moving pathways in the city. The second 
line contains six real numbers $x_1$, $y_1$, $x_2$, $y_2$, $v_1$, $v_2$, 
separated by spaces~---~the coordinates of Eddy's house and of the Council 
building, and the speed of pathways and of Eddy respectively. 
Each of the next $N$ lines contains a description of a pathway 
consisting of six real numbers 
$x_{i1}$, $y_{i1}$, $x_{i2}$, $y_{i2}$, $T^+_i$ and 
$T^-_i$, where $(x_{i1},y_{i1})$ and $(x_{i2},y_{i2})$ are two different 
points on the pathway and $0\leq T^+_i,T^-_i\leq10$ are the boarding and 
leaving times. 
All coordinates do not exceed 10000 by their absolute values, and 
$v_1$ and $v_2$ are real numbers ranging from $1$ to $100$. 
All pathways lie on different straight lines. 
Neither $(x_1,y_1)$ nor $(x_2,y_2)$ lie on any of the pathways.

\OutputFile

First line of output must contain one real number $T$ --- the 
minimal travel time required. The second line must contain 
one integer $0<M\leq 300$ --- 
the number of segments from which the optimal path is composed. 
Each of the next $M$ lines should consist of one integer $0\leq k_j\leq N$, 
the number of the pathway taken (0 means no pathway used), and of 
the coordinates $X_j$, $Y_j$ of the end of $j$-th segment of this path.
All real numbers are to be output with at least six digits after decimal point.

\Example

\begin{example}[*\stretchin{1cm}]
\exmp{
2
-100 -100 200 100 2.92893219 7.07106781
0 0 1 0 0 0
2000 0 2000 1 0 0}{
50.000000
3
0 0.000000 0.000000
1 100.000000 0.000000
0 200.000000 100.000000}%
\end{example}

\end{problem}
