## SEGVIS - Horizontally Visible Segments

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 that:

- 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 < = 8000, equal to the number of vertical line segments.

Each of the following n lines consists of exactly 3 nonnegative integers
separated by single spaces: y'_{i}, y''_{i}, x_{i}(that
is the y-coordinate of the beginning of a segment, y-coordinate of its end and
its x-coordinate, respectively). The coordinates satisfy: 0 < = y'_{i}<
y''_{i} <= 8000, 0 < = x_{i} <= 8000. 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.

### Example

1 5 0 4 4 0 3 1 3 4 2 0 2 2 0 2 3Sample input:1Sample output:

Added by: | adrian |

Date: | 2004-07-02 |

Time limit: | 3.25s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All |

Resource: | ACM Central European Programming Contest, Warsaw 2001 |