1. Write a C++ program that automatically prints all permutations of n elements, denoted as {1, 2, ..., n). At the end, report the total number permutations as well. (Hint: This problem is highly recursive and thus a recursive program is more suitable for solving this problem). Test your program by setting n to 4, and produce the following results Demonstrate your result to a TA to get the 3 score point for this homework The 1-th Pattern: (01 23) The 2-th Pattern: (0132) The 3-th Pattern: (0213) The 4-th Pattern: (023 1) The 5-th Pattern: (03 21) The 6-th Pattern: (0 312) The 7-th Pattern: (1 0 2 3) The 8-th Pattern: (1 0 3 2) The 9-th Pattern: (1203) The 10-th Pattern: (1 2 3 0) The 11-th Pattern: (1 3 20) The 12-th Pattern: (1 3 02) The 13-th Pattern: (2 103) The 14-th Pattern: (2 1 3 0) The 15-th Pattern: (2013) The 16-th Pattern: (2 03 1) The 17-th Pattern: (2 301) The 18-th Pattern: (23 1 0) The 19-th Pattern: (3 1 2 0) The 20-th Pattern: (3 10 2) The 21-th Pattern: (3 210) The 22-th Pattern: (3 201) The 23-th Pattern: (3021) The 24-th Pattern: (301 2) There are 24 permutations in total