sql HAVING max(count())返回零行

我正在尝试获得课程表重叠的教室,我的桌子:课程:

COURSE_ID    NAME
11           matematika
22           logika
33           himiya
44           sport
55           algoritmika
66           hedva
77           algebra linearit

时间表:

ID  COURSE_ID  ID_ROOM  DAY  HOUR
1   11         105      Mon  10am
2   11         105      Wen  10am
3   11         105      Thu  10am
4   22         105      Mon  10am
5   22         205      Wen  10am
6   22         105      Thu  10am
7   33         305      Mon  11am
8   33         105      Mon  10am

类_房间:

ID_ROOM  LOCATION  CAPACITY
105      A         20
205      B         10
305      C         30

我的sql是:

select class_room.ID_ROOM as crid, class_room.LOCATION, schedule.DAY as d, schedule.HOUR as h,  count(courses.COURSE_ID) as count 
  from schedule
  natural join class_room
  natural join courses
  group by crid, d, h
  order by count desc;

我得到:

crid  LOCATION  d   h       count
105   A         Mon 10am    3
105   A         Thu 10am    2
305   C         Mon 11am    1
105   A         Wen 10am    1
205   B         Wen 10am    1

但我只需要显示计数的所有最大值(目前为1行)。 我试过了

select class_room.ID_ROOM as crid, class_room.LOCATION, schedule.DAY as d, schedule.HOUR as h,  count(courses.COURSE_ID) as count 
  from schedule
  natural join class_room
  natural join courses
  group by crid, d, h
  having max(count)
  order by count desc;

但返回的是空表。 怎么了?或者,也许是另一个解决方案的建议,以获得我需要的东西?