[{"department":"emergency_care","doctors":["d1","d2","d3"],"nurses":["n1","n2","n3","n4","n5"]},{"department":"child_health","doctors":["d4","d5"],"nurses":["n6"]}]

db.collection.aggregate([{"$group":{"_id":null,"totalDoctors":{"$sum":{"$size":"$doctors"}},"totalNurses":{"$sum":{"$size":"$nurses"}}}},{"$project":{"_id":0,"nPersons":{"$add":["$totalDoctors","$totalNurses"]}}}])