type Integer {
  Integer succ();
  Integer plus(Integer y);
  Integer times(Integer y);
}

class Zero() : Integer impl Integer {

  Integer plus(Integer y) {
    return y;
  }

  Integer times(Integer y) {
    return (this : Integer);
  }
  
  Integer succ() {
    return new Positive : Integer(pred = (this : Integer));
  }

  export Integer : plus, times, succ;
}

class Positive() : Integer impl Integer {

  init Integer pred;

  Integer plus(Integer y) {
    return pred.plus(y.succ());
  }

  Integer times(Integer y) {
    return pred.times(y).plus(y);
  }

  Integer succ() {
    return new Positive : Integer(pred = (this : Integer));
  }

  export Integer : plus, times, succ;
}

Integer main() {
  Integer zero  = new Zero     : Integer();
  Integer one   = new Positive : Integer(pred = zero);
  Integer two   = new Positive : Integer(pred = one);
  Integer three = one.plus(two);
  Integer four  = two.times(two);
  Integer five  = four.plus(one);
  Integer six   = two.plus(four);
  Integer seven = one.plus(two.plus(four));
  Integer eight = two.times(two);
  Integer nine  = three.times(three);

  return nine.plus(one);
}