You are given a lot of cuboid boxes with different length, breadth and height. You need to find the maximum subset which can fit into each other (length, breadth and height of first block greater than length, breadth and height of second block).

For example:

If Box A has LBH as 7 8 9

If Box B has LBH as 5 6 8

If Box C has LBH as 5 8 7

If Box D has LBH as 4 4 4

then answer is A,B,D

Now, algorithm is first sort in terms of length, then find MIS of breadth and from previous result find MIS of height, however order can play a role here.

So, it is requested if someone can give a proper algorithm for this.