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: (0 1 2 3) The 2-th Pattern: (01 32) The 3-th Pattern: (021 3) The 4-th Pattern: (02 3 1) The 5-th Pattern: (0 3 2 1) The 6-th Pattern: (0312) The 7-th Pattern: (1 023) The 8-th Pattern: (1 032) The 9-th Pattern: (1 203) The 10-th Pattern: (1 230) The 11-th Pattern: (1 320) The 12-th Pattern: (1 302) The 13-th Pattern: (2103) The 14-th Pattern: (2130) The 15-th Pattern: (2 013) The 16-th Pattern: (2 031) The 17-th Pattern: (2301) The 18-th Pattern: (2 310) The 19-th Pattern: (3120) The 20-th Pattern: (3102) The 21-th Pattern: (3 2 1 0) The 22-th Pattern: (3 2 0 1) The 23-th Pattern: (3 0 2 1) The 24-th Pattern: (3 0 1 2) There are 24 permutations in total!