I hope this question finds you well. I have two models, 1st model of Faculty is as following:

const facultySchema = new mongoose.Schema(
  {
    _id: mongoose.Schema.Types.ObjectId,
    name: {
      type: String,
      required: [true, "le nom de la faculté est obligatoire"],
    },
    code_name: {
      type: String,
      required: [true, "l‘abréviation est obligatoire"],
    },
    programs: [
      {
        type: mongoose.Schema.Types.ObjectId,
        ref: "Program",
      },
    ],
  }
);

and here Program model

const programSchema = new mongoose.Schema(
  {
    _id: mongoose.Schema.Types.ObjectId,
    name: {
      type: String,
      required: [true, "le nom est obligatoire"!],
    },
    faculties: [
      {
        type: mongoose.Schema.Types.ObjectId,
        ref: "Faculty",
      },
    ],
  },
  {
    timestamps: true,
  }
);

I want to add a middleware so that when I update a program by removing or adding an element in the faculties array, it will be automatically removed or added in programs field according to the faculty_id removed. and vis-versa if a faculty is updated by removing or adding an element in programs field, the faculty should be added or removed accordingly in the faculties field in the program related. I know about the pre and post middleware but I don't know how to do this specific update cascading please help me, this is really important to me. thank you so much.