For each of the following problems, you need to find a recursive solution. For problems involving NaturalNumber, use only the kernel methods. Do not use "tricks" like converting a NaturalNumber into a String and then solving the problem on the String.

1. Implement the static method declared as follows:

   /**

   * Returns the number of digits of {@code n}.

   *

   * @param n

   * {@code NaturalNumber} whose digits to count

   * @return the number of digits of {@code n}

   * @ensures numberOfDigits = [number of digits of n]

   */

   private static int numberOfDigits(NaturalNumber n) {...}

2. Implement the static method declared as follows:

   /**

   * Returns the sum of the digits of {@code n}.

   *

   * @param n

   * {@code NaturalNumber} whose digits to add

   * @return the sum of the digits of {@code n}

   * @ensures sumOfDigits = [sum of the digits of n]

   */

   private static int sumOfDigits(NaturalNumber n) {...}

3. In addition to the kernel methods, for this question (only!) you are allowed to use the NaturalNumber method add. Implement the static method declared as follows:

   /**

   * Returns the sum of the digits of {@code n}.

   *

   * @param n

   * {@code NaturalNumber} whose digits to add

   * @return the sum of the digits of {@code n}

   * @ensures sumOfDigits = [sum of the digits of n]

   */

   private static NaturalNumber sumOfDigits(NaturalNumber n) {...}

4. Implement the static method declared as follows:

   /**

   * Divides {@code n} by 2.

   *

   * @param n

   * {@code NaturalNumber} to be divided

   * @updates n

   * @ensures 2 * n <= #n < 2 * (n + 1)

   */

   private static void divideBy2(NaturalNumber n) {...}

5. Implement the static method declared as follows:

   /**

   * Checks whether a {@code String} is a palindrome.

   *

   * @param s

   * {@code String} to be checked

   * @return true if {@code s} is a palindrome, false otherwise

   * @ensures isPalindrome = (s = rev(s))

   */

   private static boolean isPalindrome(String s) {...}