Global Positioning System

Time Limit
1s
Memory Limit
65536KB
Judge Program
Standard
Ratio(Solve/Submit)
0.00%(0/0)
Description:

Xed has a great interest in Global Positioning System. To simulate it, he constructs a Cartesian coordinate system in a infinite plane whose one unit equals 1 kilometer. Then Xed puts three sensors on three different points (x1,y1), (x2,y2), (x3,y3) and a signal generator in the plane.

All three sensors are linked to a timer. Once a sensor has received the signal it will immediately trigger the timer which records the time. The timer starts to count when it first receives a trigger and records the earliest time when the sensors receive a signal.

Now you are given:

  1. positions of the sensors: (x1,y1), (x2,y2), (x3,y3)
  2. time records: t1, t2, t3 seconds. (t1, t2, t3 ≥ 0, and at least one equals 0 which presents the first sensor triggers the timer)
  3. Velocity of the signal: C meters per second (C > 0)

Please help Xed to determine the position of the signal generator. It is guaranteed that such point always exists and is unique.

Input:

The input consists of several test cases. Each test case has the following format:
C
x1 y1 x2 y2 x3 y3
t1 t2 t3
The input is terminated by C = 0

Output:

For each test case, print the case number on the first line and the position of the generator (x, y) on the second line. x and y should be separated by a single space and should be rounded to six digits to the right of the decimal point. See the sample output below for more details.
　

Sample Input:
1000
0 0 1 0 2 1
0 0.414213562373 1

1000
0 1 1 1 2 1
0 0.6 1.6

1000
0 0 0 1 1 0
0.4142135 0 0
1000
0 0 0 -1 0 1
0 0 1

1000
0 0 0 1 0 -1
0 1 0
1000
0 0 1 0 -1 0
0 1 0
1000
0 0 -1 0 1 0
0 0 1
100
0 0 0 1 1 0
0 10 10
0
Sample Output:
Case 1:
0.000000 1.000000
Case 2:
0.200000 1.000000
Case 3:
1.000000 1.000000
Case 4:
0.000000 -0.500000
Case 5:
0.000000 -0.500000
Case 6:
-0.500000 0.000000
Case 7:
-0.500000 0.000000
Case 8:
0.000000 0.000000
Submit