Write a C++ program that reads a number of elements in a set and then read the elements of the set. After that, your program should display all possible binary numbers and corresponding subsets one by one. For the program, you can assume that the number of elements in a set is less than 10.

Sample Run 1: Assume that the user typed the following input. Note that there are three elements in the set with the elements A, B, and C.

3 A B C

This is the correct output.

000:EMPTY 001:C 010:B 011:B C 100:A 101:A C 110:A B 111:A B C

The first line shows that the binary number is 000. Note that the first bit 0 is for the element A, the second bit 0 for the element B, and the last bit 0 for the element C. Since all three bits are 0, the binary number 000 means the empty set. The next line indicates that the binary number is 001 and it corresponds to the subset {C} because only the last bit is 1. Similarly, the last line indicates that the binary number is 111 and it corresponds to the subset {A, B, C} because all bits are 1.

Sample Run 2: Assume that the user typed the following input.

2 ABC123 ABC321

This is the correct output.

00:EMPTY 01:ABC321 10:ABC123 11:ABC123 ABC321