如果不知道子文档的嵌套级别，如何获得子文档？

Question

这是对my previous question的后续任务。

我有以下mongoDB文档结构

School1
    Division1
        Classroom1
            Student1 last name
            Student2 last name
        Classroom2
            < empty classroom >
        Student3 last name
        Student4 last name

    Divison2
        Classroom1
            -
        Classroom2
            -
School2
    -
        -
        -
    -
    -

我需要的是以下形式的结果：

{
    school: school1,
    division: division1,
    classroom: classroom1,
    student: student1,
},
...
{
    school: school1,
    division: division1,
    student: student3,
}

现在我正在做

db.collection.aggregate(
[
      {$unwind:"$schools"},
      {$unwind:"$school.divisions"},
      {$unwind:"$school.divisions.classrooms"},
    {
        $project: {
            school: "$schools._id",
            division: "$school.divisions._id",
            classroom: "$school.divisions.classrooms._id",
            student: "$school.divisions.classrooms.students._id"
        }
    },
    {$unwind:"$student"}
]
)

但是我没有得到所需的东西，因为不是所有的学生都在教室里，而是直接在一个部门里。无论嵌套级别如何，我都需要查询来获取学生。

什么是一个好的方法？

编辑1 ：收藏集如下所示：

{
    "_id" : "school1",
    "divisions": [
        {
            "_id": "division1",
            "classrooms" : [
                "_id": "classroom1",
                "students" : [
                    {
                        student1
                    },
                    {
                        student2
                    }
                ]
            ]
            "students" : [],
        },
        {
            "_id": "division2",
            "classrooms:" [],
            "students": [
                {
                    student3
                },
                {
                    student4
                }
            ]
        }
    ]
    }
}