Treasure Hunt 

Archeologists from the Antiquities and Curios Museum (ACM) have flown to Egypt to examine the great pyramid of Key-Ops. Using state-of-the-art technology they are able to determine that the lower floor of the pyramid is constructed from a series of straightline walls, which intersect to form numerous enclosed chambers. Currently, no doors exist to allow access to any chamber. This state-of-the-art technology has also pinpointed the location of the treasure room. What these dedicated (and greedy) archeologists want to do is blast doors through the walls to get to the treasure room. However, to minimize the damage to the artwork in the intervening chambers (and stay under their government grant for dynamite) they want to blast through the minimum number of doors. For structural integrity purposes, doors should only be blasted at the midpoint of the wall of the room being entered. You are to write a program which determines this minimum number of doors.

An example is shown below:

Input 

The input will consist of several cases.The first line of the input contains the number of cases, and it's followed bya blank line.

The first line of each case will be an integer n ( $0 \leŸ n \leŸ 30$) specifying number of interior walls, followed by n lines containing integer endpoints of each wall x₁ y₁ x₂ y₂. The 4 enclosing walls of the pyramid have fixed endpoints at (0,0), (0,100), (100,100) and (100,0) and are not included in the list of walls. The interior walls always span from one exterior wall to another exterior wall and are arranged such that no more than two walls intersect at any point. You may assume that no two given walls coincide. After the listing of the interior walls there will be one final line containing the floating point coordinates of the treasure in the treasure room (guaranteed not to lie on a wall).

Different cases are separated by a blank line.

Output 

For each case, print a single line listing the minimum number of doors which need to be created, in the format shown below. Print a blank line between cases.

Sample Input 

1

7
20 0 37 100
40 0 76 100
85 0 0 75
100 90 0 90
0 71 100 61
0 14 100 38
100 47 47 100
54.5 55.4

Sample Output 

Number of doors = 2