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Time Limit: 3000 MS    Memory Limit: 65536 K

Description

A windstorm has knocked over a beekeeper's hive boxes. A hive box contains a
number of panels. Each panel contains a honeycomb. The panels are thin enough
that the bees create a single layer of hexagonal cells in each panel. All cells
are hexagonal and of uniform size.

Upon inspecting the panels, the beekeeper discovers that many of the hexagonal
cells have been damaged. Given as input a list of line segments representing
undamaged cell walls, compute the number of undamaged (i.e. containing all six
walls) hexagons in the panel. You can assume that the only damage to the
honeycomb is that some cell walls are missing, but none of them are moved, broken
in half, etc. Below is an example honeycomb with the undamaged hexagons shaded in
gray:

Input

Input to this problem will begin with a line containing a single integer N (1 ¡Ü
N ¡Ü 100) indicating the number of data sets. Each data set begins with a line
containing a single integer S (1 ¡Ü S ¡Ü 1000) specifying the number of line
segments in the data set. This is followed by S lines of the form "X1,Y1 X2,Y2"
which specify the individual cell walls of the honeycomb. Each coordinate is a
floating point number greater than or equal to zero but less than or equal to
1000 and with at most 3 digits after the decimal point (i.e. rounded to the
nearest thousandth). The coordinates will not use "exponent notation" such as
"3.123e+3".

You can make the following assumptions about the input:

1.The length of each cell wall is 1 unit
2.The honeycomb will have the same orientation as the example figure. In other
3.words, if the top or bottom cell walls of a unit are present, they will be always
parellel to the x-axis.
There will be no duplicate or overlapping cell walls. The line segments can only
touch each other at the endpoints.

Output

For each data set, print the number of undamaged hexagonal cells that were detected.

Sample Input

2
6
0.500,1.866 1.500,1.866
0.000,1.000 0.500,1.866
1.500,0.134 2.000,1.000
1.500,1.866 2.000,1.000
0.500,0.134 1.500,0.134
0.000,1.000 0.500,0.134
3
1.500,1.866 2.000,1.000
0.500,0.134 1.500,0.134
0.000,1.000 0.500,0.134

Sample Output

1
0

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