Write SQL query to solve given problem: Among the trains that run in the east direction, how many of them have more than 2 long cars?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT SUM(CASE WHEN T2.longCarsNum > 2 THEN 1 ELSE 0 END)as count FROM trains AS T1 INNER JOIN ( SELECT train_id, COUNT(id) AS longCarsNum FROM cars WHERE len = 'long' GROUP BY train_id ) AS T2 ON T1.id = T2.train_id WHERE T1.direction = 'west'