Problem 2. Data Cube Concepts (26 points) Suppose the base cuboid of this data cube contains two cells: (a1,a2,a3,a4,a5,a6,a7):1,(a1,b2,a3,b4,a5,b6,a7):1 where ai=bi for i=2,4,6. Assume each dimension contains no concept hierarchy. (1) (6 points) Please list all the (nonempty) closed cells in this data cube. (2) (4 points) How many (nonempty) aggregate cells are there in this data cube? (3) (4 points) How many (nonempty) aggregate closed cells are there in this data cube? Please list them. (4) (4 points) If we set minimum support =2, how many (nonempty) aggregate cells are there in the corresponding iceberg cube? (5) (8 points) What are the differences among star schema, snowflake schema, and fact constellations for modeling the data warehouses? Which schema do you suggest to model this cube? Please justify your