Write SQL query to solve given problem: Among the active businesses in Arizona, how many businesses work after 12PM?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT COUNT(DISTINCT T2.business_id) FROM Business_Hours AS T1 INNER JOIN Business AS T2 ON T1.business_id = T2.business_id INNER JOIN Business_Categories AS T3 ON T2.business_id = T3.business_id INNER JOIN Categories AS T4 ON T3.category_id = T4.category_id WHERE T2.active = 'true' AND T2.state = 'AZ' AND T1.opening_time > '12PM'