@atul-I think This Should work for n dimension-
complexity O(n^no.of dimesions)
:-
have N-dimension check for which Tile can contain which Tile.i.e (3,3,4)
can contain (2,3,4) .
Now
 1.Take the titles which cannot contain any-other tile set no-of tile if it
is base =1;
2.now take tiles which can contain 1 tile only.This tile will contain any
of tiles in 1. case ..it cannot be other title..since other tile can
contain tiles>=1 which means it shud contain >=2..which is not true.
set with base value=(if it exist)1+1=2;
3.similarly for other Tiles..in increasing order check maximum tile it can
contain..

correct me if wrong...complexity is high but its due to no.of dimesion..for
n=2 its simply O(n^2)..

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