Write a recursive method called writeNumbers that takes an integer n as a parameter and that writes the first n numbers separated by commas with the odd numbers in descending order followed by the even numbers in ascending order. For example, the call:

writeNumbers(5);

should produce the following output:

5, 3, 1, 2, 4

The odd numbers (5, 3, and 1) appear first in descending order followed by the even numbers (2 and 4) in ascending order. Notice that commas are used to separate consecutive values in the list. Your method should send its output to System.out and should not call println. For example, the following calls:

writeNumbers(5);

System.out.println(); // to complete the line of output

writeNumbers(1);

System.out.println(); // to complete the line of output

writeNumbers(8); System.out.println(); // to complete the line of output

should produce exactly three lines of output:

5, 3, 1, 2, 4

1

7, 5, 3, 1, 2, 4, 6, 8

You must exactly reproduce the format of these examples. Your method should throw an IllegalArgumentException if passed a value less than 1. You are not allowed to construct any structured objects (no array, ArrayList, String, StringBuilder, etc) and you may not use a while loop, for loop, or do/while loop to solve this problem; you must use recursion.