## POLY1 - Polygon

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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.

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: Michał Czuczman Date: 2004-08-10 Time limit: 5s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All Resource: 5th Polish Olympiad in Informatics, stage 1 (Krzysztof Diks)