Medium

23.53%

You are given a set of N types of rectangular 3-D boxes, where the ith box has height h, width w and length l. You task is to create a stack of boxes which is as tall as possible, but you can only stack a box on top of another box if the dimensions of the 2-D base of the lower box are each strictly larger than those of the 2-D base of the higher box. Of course, you can rotate a box so that any side functions as its base.It is also allowable to use multiple instances of the same type of box. You task is to complete the function **maxHeight** which returns the height of the highest possible stack so formed.

**Input:**

The first line of input contains an integer T denoting the no of test cases then T test cases follow . Each test case contains an integer N denoting the total no of boxes available. In the next line are 3*N space separated values denoting the height width and length of the N boxes.

**Output:**

For each test case in a new line output will be the highest possible stack height which could be formed.

**Constraints:**

1<=T<=100

1<=N<=100

1<=l,w,h<=100

**Example (To be used for expected output) :
Input:**

2

4

4 6 7 1 2 3 4 5 6 10 12 32

3

1 2 3 4 5 6 3 4 1

60

15