Write SQL query to solve given problem: Between the faculty employee professors, how many teaches high-level or harder undergraduate courses? Indicate each of the professors unique identifying number.. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT COUNT(*) FROM person AS T1 INNER JOIN taughtBy AS T2 ON T1.p_id = T2.p_id INNER JOIN course AS T3 ON T3.course_id = T2.course_id WHERE T1.hasPosition = 'Faculty_eme' AND T1.professor = 1 AND T3.courseLevel = 'Level_400'