There are n people in a room, where n is an integer greater than or equal to 1. Each person shakes hands once with every other person. What is the total number, h(n), of handshakes? Use recursion to solve this problem. To get you started, if there are only one or two people in the room, then

handshake(1) = 0

handshake(2) = 1

If a third person enters the room, he or she must shake hands with each of the two people already there. This is two handshakes in addition to the number of handshakes that would be made in a room of two people, or a total of three handshakes.

If a fourth person enters the room, he or she must shake hands with each of the three people already present. This is three handshakes in addition to the number of handshakes that would be made in a room of three people, or six handshakes.

Write a program that gets the number of people as user input, and outputs the number of handshakes.

NOTE: Your implementation must include the definition/implementation and use/calling of the recursive method howManyHandshakes that is passed the (integer) number of people to its parameter variable, and returns the number of handshakes, using the above scheme.

Use the Design Recipe to design the algorithm for each method (main and others), showing all work as comments in the source code (.java) file.

Using Eclipse, implement the algorithm as a program.