Guarding the columns

Time Limit: 8 Seconds    Memory Limit: 65536 KB

Persepolis is one of the historical and fascinating sites in Iran. As you know, there are numerous columns of stone in this capital of the great ancient Iran. More specifically, there are K columns in Persepolis that have  circular,  rectangular  and  triangular  bases.  These  columns  are  built  perfectly  straight.  In  other words, if you look at them from sky you may only see the perimeter of their bases. Also, some of these columns may have intersections as depicted in the following figure. 


The  men  in  charge  of  maintenance  of  columns  want  to  create  a  safe  area  around  columns.  For  this purpose they have planted a number of N rods (small irony columns) in the ground. They start from a specific rod, tie the rope to it and continue by tying the rope to the next rod and so until they reach the first  rod  again.  The  rope  between  two  consecutive  rods  should  be  fully  straight,  but  it  can  touch  the columns. Consequently one safe and closed area will be formed around all columns in it. 

Now the maintenance team wants to know if it is possible to create the safe surrounding using only the existing rods. If it is possible, find is the minimum length of the rope needed to create it? Note that all columns must be surrounded in one connected safe area.

 

Input

The first line contains an integer T (T ≤ 100), the number of test cases. The first line of each test contains integer N (3 ≤ N ≤ 300), the number of rods. Then N lines follow, i‐th of which contains two integers xi, yi, the coordinates of i‐th rod.  

In the next line there is an integer K (1 ≤ K ≤ 300), the number of columns. Then K lines follow, each line represent one of the columns. i‐th of these lines starts with a character B. If B is equal to ‘C’, it means the column’s base is a circle and it follows with three integers x, y, r (1 ≤ r ≤ 104)  —the coordinates of center and the radius of the base of column, respectively. If B is equal to ‘T’ it means the column’s base is a triangle and it follows with six integers x1, y1, x2, y2, x3, y3 that represent the coordinates of vertices of column’s base. And if B is equal to ‘R’ it means the column’s base is a rectangle and it follows with four integers x1, y1,  x2, y2  the  coordinates of the lower left and  the  upper right vertices of the base of column, respectively. 

 All  coordinates  are  integers  with  their  absolute  values  less  than  or  equal  to  10000.  Also  rods  are different and do not coincide with columns. All columns have positive area. 

Output

For each test, if it is possible to create a safe area using existing rods, output the minimum length of the rope  rounded  to  three  digits  after  the  decimal  point.  Otherwise  print  “Impossible”.  (Quotes  for clarity) 

 

Sample Input

2
4
2 2
6 2
5 5
3 5
1
C 4 3 1
5
6 4
9 8
8 9
3 9
3 8
3
C 6 7 1
T 5 8 7 8 6 9
R 4 6 6 9

Sample Output

12.325
Impossible
Submit

Source: AUT 2012