## EMPTY - Empty Cuboids

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We call a cuboid regular if:

• one of its vertices is a point with coordinates (0,0,0),
• edges beginning in this vertex lie on the positive semi-axes of the coordinate system,
• the edges are not longer than 106

There is given a set A of points of space, whose coordinates are integers from the interval [1..106]. We try to find a regular cuboid of maximal volume which does not contain any of the points from the set A. A point belongs to the cuboid if it belongs to the interior of the cuboid, i.e. it is a point of the cuboid, but not of its wall.

Write a program which:

• reads from the standard input the coordinates of points from the set A,
• finds one of the regular cuboids of maximal volume which does not contain any points from the set A,
• writes the result to standard output.

### Input

Input begins with a line containing integer t<=10, the number of test cases. t test cases follow.

In the first line of each test case one non-negative integer n is written ( n <= 5000). It is the number of elements in the set A. In the following n lines of the input there are triples of integers from the interval [1..106], which are the X, Y and Z coordinates of points from A, repectively. Numbers in each line are separated by single spaces.

### Output

For each test case there should be three integers separated by single spaces. These are the X, Y and Z coordinates (respectively) of the vertex of the regular cuboid of maximal volume. If there is more than one such a cuboid, choose whichever. We require that all coordinates be positive.

### Example

```Sample input:
1
4
3 3 300000
2 200000 5
90000 3 2000
2 2 1000

Sample output:
1000000 200000 1000
```