PeanoNumbers

Peano numbers are a simple way of representing the natural numbers using only a zero value and a successor function. We can represent Peano numbers as follows:

interface Peano {
  final class Zero implements Peano {
    static Zero INSTANCE = new Zero();
    private Zero() {}
  }

  final class Succ implements Peano {
    final Peano peano;
    Succ(Peano peano) {
      this.peano = peano;
    }
  }
}

where:

• 0 is represented by Zero.INSTANCE
• 1 is represented by Succ(Zero.INSTANCE)
• 2 is represented by Succ(Succ(Zero.INSTANCE))
• 3 is represented by Succ(Succ(Succ(Zero.INSTANCE)))

etc. Your mission in this Kata is to implement the following static operations with peano numbers:

• add(Peano a, Peano b) Addition
• sub(Peano a, Peano b) Subtract (ArithmeticException: "negative number")
• mul(Peano a, Peano b) Multiplication
• div(Peano a, Peano b) Integer division (ArithmeticException: "divide by 0")
• even(Peano a) Even number
• odd(Peano a) Odd number
• compare(Peano a, Peano b) Compare (LT, GT or EQ)

IMPORTANT NOTE: -You can't use the following characters: + - * / % > < -You can't skip this rule by using libraries like Math or BigDecimal