(Game: nine heads and tails) Nine coins are placed in a 3×3 matrix with some face up and s...

(Game: nine heads and tails) Nine coins are placed in a 3×3 matrix with some face up and some face down. You can represent the state of the coins using a 3×3 matrix with values 0 (head) and 1 (tail). Here are some examples:

Each state can also be represented using a binary number. For example, the preceding matrices correspond to the numbers

000010000 101001100 110100001 101110100 100111110

The total number of possibilities is 512. So you can use decimal numbers 0, 1, 2, 3 ,... , and 511 to represent all states of the matrix. Write a program that prompts the user to enter a number between 0 and 511 and displays the corresponding matrix with characters H and T. Here is a sample run:

The user entered 7 , which corresponds to 000000111. Since 0 stands for H and 1 for T , the output is correct.