Mongoose get collection, where ref

Question

I have two schemas: Pages and Posts.

var pageSchema = new Schema({
    commented_times: {
        type: Number,
        default: 0
    },
    posts: {
        type: Schema.Types.ObjectId,
        ref: 'Post'
    }
});



var postSchema = new Schema({
    page: [{
        type: Schema.Types.ObjectId,
        ref: 'Page'
    }]
});

I want to get all Posts, where commented_times in Page is lover than 3, how do I do that?

I tried the following, but it is not working.

return Post.find({}).populate({
    path: 'page',
    match: {
        commented_times: {
            $lt: 3
        }
    },
}).sort({
    rating: -1
}).limit(5);