POLY1 - Polygon

We say that two triangles intersect if their interiors have at least one common point. A polygon is called convex if every segment connecting any two of its points is contained in this polygon. A triangle whose vertices are also vertices of a convex polygon is called an elementary triangle of this polygon. A triangulation of a convex polygon is a set of elementary triangles of this polygon, such that no two triangles from the set intersect and a union of all triangles covers the polygon. We are given a polygon and its triangulation. What is the maximal number of triangles in this triangulation that can be intersected by an elementary triangle of this polygon?

Example

Consider the following triangulation:

The elementary triangle (1,3,5) intersects all the triangles in this triangulation.

Task

Write a program that for each test case:

  • reads the number of vertices of a polygon and its triangulation;
  • computes the maximal number of triangles intersected by an elementary triangle of the given polygon;
  • writes the result to standard output.

Input

The number of test cases t is in the first line of input, then t test cases follow separated by an empty line

In the first line of a test case there is a number n, 3 <= n <= 1000, which equals the number of vertices of the polygon. The vertices of the polygon are numbered from 0 to n-1 clockwise. The following n-2 lines describe the triangles in the triangulation. There are three integers separated by single spaces in the (i+1)-st line, where 1 <= i <= n-2. These are the numbers of the vertices of the i-th triangle in the triangulation.

Output

For each test case your program should produce one line with exactly one integer - the maximal number of triangles in the triangulation, that can be intersected by a single elementary triangle of the input polygon.

Example

Sample input:
1
6
0 1 2
2 4 3
0 5 4
2 4 0

Sample output:
4

Added by:MichaƂ Czuczman
Date:2004-08-10
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:C C++ 4.3.2 CPP CPP14 CPP14-CLANG FORTRAN JAVA NODEJS PERL6 PERL PHP PROLOG PYTHON PYTHON3 RUBY TCL
Resource:5th Polish Olympiad in Informatics, stage 1 (Krzysztof Diks)

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