Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE CAR_NAMES (model VARCHAR)
TABLE: CREATE TABLE MODEL_LIST (Maker VARCHAR, model VARCHAR)
TABLE: CREATE TABLE CAR_MAKERS (Id VARCHAR, Maker VARCHAR)

### Question ###
What are the ids and makers of all car makers that produce at least 2 models and make more than 3 cars?

### Accurate SQL ###

SELECT T1.Id, T1.Maker FROM CAR_MAKERS AS T1 JOIN MODEL_LIST AS T2 ON T1.Id = T2.Maker GROUP BY T1.Id HAVING COUNT(*) >= 2 INTERSECT SELECT T1.Id, T1.Maker FROM CAR_MAKERS AS T1 JOIN MODEL_LIST AS T2 ON T1.Id = T2.Maker JOIN CAR_NAMES AS T3 ON T2.model = T3.model GROUP BY T1.Id HAVING COUNT(*) > 3