Sql 如何使用Clickhouse的COUNT聚合返回所有列，但GROUP BY是这些列的子集

我试图在ClickHouse中返回表中的所有列，但是我想将Program中的students作为一个字段进行计数.理想情况下，查询应该返回University, Student, Program, student_count.计数将是有多少个‘程序’以University为单位进行分组.下面是一个查询示例

SELECT 
    University,
    Program, 
    Student,
    COUNT(Program) as student_count
FROM 
    table
GROUP BY 
    University

示例数据:

| University  | Student   | Program   |
| ----------- | --------- | --------- |
| University A| Student 1 | Program A |
| University A| Student 2 | Program A |
| University A| Student 3 | Program B |
| University B| Student 4 | Program A |
| University B| Student 5 | Program B |

所需日期:(用谷歌翻译翻译)

| University  | Student  |Program   |student_count|
| ----------- | ---------| -------- | ----------- | 
| University A| Student 1| Program A|2            |
| University A| Student 2| Program A|2            |
| University A| Student 3| Program B|1            |
| University B| Student 4| Program A|1            |
| University B| Student 5| Program B|1            |

我的问题是，ClickHouse有可能做到这一点吗？如果可能，它将如何实现？