MongoDB | Too many positional (i.e. '$') elements found in path

I have a scheme with nested arrays. I want to push an element to the 2rd dimension array. How can I do?

//working
db.findOneAndUpdate({_id:req.params._universtiyid,'faculties._id':req.params._facultiesid},
    { $push:
        {  'faculties.$.points':point}},


//not working
db.findOneAndUpdate({_id:req.params._universtiyid,'faculties._id':req.params._facultiesid},
    { $push:
        {  'faculties.$.department.$.points':points}},

//schema
faculties:[
        {   
            name:{type:String},
            department:[
                {
                    name:{type:String},
                    points:[]
                }
            ]
        }
    ],