db.st.aggregate({$project: {name: 1, classes:1}},
                {$unwind: "$classes"},
                {$group: { _id: "$classes",roster: {$push: "$name"}
                         } },
		{$project: {_id:0, class:"$_id", roster:1}},	
                {$sort: {class: 1}} )




db.st.aggregate({$unwind: { path:"$classes",
                            includeArrayIndex: "idx"}
                },
                {$unwind: { path:"$scores",
                            includeArrayIndex: "sidx"}
                },
		{$project: {name:1, class:"$classes",
                            scores:1, 
                            diff: {$subtract: ["$idx", "$sidx"]}
                            } },
                {$match: {diff: 0, class:365}},
                {$project:{name:1, class:1, score:"$scores"}}
               )


db.st.aggregate({$unwind: { path:"$classes",
                            includeArrayIndex: "idx"}
                },
                {$unwind: { path:"$scores",
                            includeArrayIndex: "sidx"}
                },
		{$project: {name:1, class:"$classes",
                            scores:1, 
                            diff: {$subtract: ["$idx", "$sidx"]}
                            } },
                {$match: {diff: 0}},
                {$project:{name:1, class:1, score:"$scores"}},
		{$group: {_id: "$class", 
                         avScore: {$avg: "$score"},
                         stDev: {$stdDevPop: "$score"}
                         }
                }
               )



db.st.aggregate({$group: {_id: "$gpa",
                          count: {$sum: 1}
                         }},
                {$sort: {_id: -1}},
                {$limit: 1}
                )
                 
db.st.aggregate({$group: {_id: "$gpa",
                          count: {$sum: 1},
                          folks:{$push: "$name"}
                         }},
                {$sort: {_id: -1}},
                {$limit: 1}
                )
     
db.st.aggregate({$group: {_id: 1, mGpa: {$max: "$gpa"}
                         }
                 })      

db.st.aggregate({$group: {_id: 1, mGpa: {$max: "$gpa"},
                   folks: {$push: {name: "$name", gpa:"$gpa"}}      
                         }
                 },
                 {$unwind: "$folks"})


db.st.aggregate({$unwind: "$scores"},
                {$bucket: {
                            groupBy: "$scores",
			    boundaries: [50, 75, 90, 100],
                            default: "other",
                 output: { count: {$sum: 1},
                           name: {$addToSet: "$name"}}
                          }
                 }
               )	

db.st.aggregate({$unwind: "$courses"},
                {$lookup: { from: "prof",
                            localField: "courses",
                            foreignField: "course",
                            as: "professors"
                           }
                }
                )