[{"_id":123,"index":"111","students":[{"firstname":"Mark","lastname":"Smith"}]},{"_id":456,"index":"222","students":[{"firstname":"Mark","lastname":"Smith"}]},{"_id":789,"index":"333","students":[{"firstname":"Neil","lastname":"Smith"},{"firstname":"Sofia","lastname":"Smith"}]}]

db.collection.aggregate([{"$match":{index:{"$in":["111","333"]}}},{"$addFields":{"students_size":{"$size":"$students"}}},{"$sort":{students_size:1}},{"$limit":1}])