Given a strictly convex polygon with vertices , , , in counterclockwise. Denote as the polygon with vertices , , , . For each , , , , find the lines which is symmetric about.

输入描述:

There are multiple test cases. The first line of input contains an integer (), the number of test cases. For each test case:

The first line contains an integer  (), the number of vertices.

The -th of the following  lines contains two integers ,  (, ) - the coordinates of .

It is guaranteed that the vertices are given counterclockwise, and the polygon is strictly convex, i.e., no three vertices are colinear.

It is guaranteed that the sum of  in all test cases does not exceed .

输出描述:

For each test case:

For each , , , , output an integer  -- the number of lines which  is symmetric about in the first line, and  lines follow.

In each of the following  lines, output three integers , ,  (, , ), denoting that  is symmetric about the line .

If there are multiple answers, you can output any of them. For each , you can output the lines in any order.

3
4
0 0
1 0
1 1
0 1
3
0 0
3 0
1 1
4
-1000000000 -1000000000
1000000000 -1000000000
1000000000 1000000000
-1000000000 1000000000

1
1 1 -1
4
1 -1 0
0 2 -1
2 0 -1
1 1 -1
0
1
1 1 0
4
1 -1 0
0 1 0
1 0 0
1 1 0