Migrated from Lutece 307 I Hate Noise!

All parts of this problem, including description, images, samples, data and checker, might be broken. If you find bugs in this problem, please contact the admins.

Description

As we all know, Fish hates noise so much. He feels very uncomfortable when he stays in a noisy place. But unfortunately,there is an airport near the campus.The aircrafts' noise always comes out when Fish is coding,which drives him crazy! Fish is so helpless, he can do nothing but to bear.

Now Fish is in his dormitory, the cartesian coordinate of his dormitory is $(x,y)$. Now an aircraft is going to take off, and Fish knows the range of the aircraft's noise influence is a circle and its radius is $r$, and the speed of the aircraft is $v$, the start point $(x_1,y_1)$ and the end point $(x_2,y_2)$ of the route (The route is a straight line). He wants to know how much time he must cost to bear that noise, can you tell him?

Input

The first line of the input contains one integer $T$($T\leq 50000$), which indicates the number of test cases.

Following each test, there is two lines. In the first line of each case, there are four real numbers $r$,$v$,$x$ and $y$($0<r,x,y<1000$, $0<v<100$), in the next line, there are four real numbers $x_1$,$y_1$,$x_2$ and $y_2$($0<x_1,y_1,x_2,y_2<1000$).

Output

For each test case, output one line. First ,output Case #C: , where $C$ is the number of test case, from $1$ to $T$. Then,output the time Fish must bear that noise, rounded two digits.

Samples

1
2.0 1.0 0.0 0.0
-3.0 0.0 3.0 0.0

Case #1: 4.00

Note

This picture shows the details of the description

Resources

Fish