Box Stacking Problem Statement

Consider you are provided with 'n' different types of rectangular 3D boxes. For each type of box, you have three separate arrays: height, width, and length that define the dimensions of the boxes. Specifically, the i^th type of box dimensions are given by height[i], width[i], and length[i].

Your task is to stack these boxes to achieve the maximum possible height.

Input:

The first line contains an integer ‘T’, the number of test cases.
For each test case, the input is structured as follows:
1. An integer ‘n’, the number of box types.
2. ‘n’ space-separated integers that specify the height array.
3. ‘n’ space-separated integers that specify the width array.
4. ‘n’ space-separated integers that specify the length array.

Output:

For each test case, output a single integer, representing the height of the tallest stack possible.

Example:

Input:

1
3
4 1 4
6 2 5
7 3 6

Output:

15

Explanation:

The boxes can be rotated to allow any face to be the base. Using rotations, the maximum height stack can be formed with the dimensions given.

Constraints:

• 1 <= T <= 50
• 1 <= n <= 10²
• 1 <= height[i] <= 10²
• 1 <= width[i] <= 10²
• 1 <= length[i] <= 10²
• Time limit: 1 second

Note:

The following rules apply when stacking:

• You can only place a box on top of another if its base dimensions (length and width) are strictly smaller than the box beneath it.
• Boxes can be rotated to use any face as the base, and you can use multiple copies of the same box, resulting in different possible orientations for each type.
• No two boxes will have all three dimensions identical.