Horizontally Visible Segments

Time Limit: 10 Seconds
Memory Limit: 32768 KB

There is a number of disjoint vertical line segments in the plane. We say that
two segments are horizontally visible if they can be connected by a horizontal
line segment that does not have any common points with other vertical segments.
Three different vertical segments are said to form a triangle of segments if
each two of them are horizontally visible. How many triangles can be found in
a given set of vertical segments?

**Task**

Write a program which for each data set:

reads the description of a set of vertical segments,

computes the number of triangles in this set,

writes the result.

**Input**

The first line of the input contains exactly one positive integer d equal to
the number of data sets, 1 <= d <= 20. The data sets follow.

The first line of each data set contains exactly one integer n, 1 <= n <=
8 000, equal to the number of vertical line segments.

Each of the following n lines consists of exactly 3 nonnegative integers separated
by single spaces:

yi', yi'', xi - y-coordinate of the beginning of a segment, y-coordinate of
its end and its x-coordinate, respectively. The coordinates satisfy 0 <=
yi' < yi'' <= 8 000, 0 <= xi <= 8 000. The segments are disjoint.

**Output**

The output should consist of exactly d lines, one line for each data set. Line
i should contain exactly one integer equal to the number of triangles in the
i-th data set.

**Sample Input**

1

5

0 4 4

0 3 1

3 4 2

0 2 2

0 2 3

**Sample Output**

1

Source:

**Central Europe 2001**
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