abstract class Nat {
    def isZero: Boolean;
    def predecessor: Nat;
    def succesor: Nat = new Succ(this)
    def + (that: Nat): Nat;
    def - (that: Nat): Nat;
    override def toString: String = {
      var i = 0;
      var n: Nat = this;
      while(n != Zero){
        n = n.predecessor
        i = i + 1
      }
      i + ""
    }
}
object Zero extends Nat{
  def isZero = true
  def predecessor = throw new Error("negative number")
  def + (that: Nat) = that;
  def - (that: Nat) = if(that == Zero) this else throw new Error("Negative number")
}
class Succ(n: Nat) extends Nat{
  def isZero = false
  def predecessor = n;
  def + (that: Nat) = new Succ(n + that)
  def - (that: Nat) = if(that.isZero) this else n - that.predecessor
}