Suppose N people want to communicate with each of N-1 other people using symmetric key encryption. All communication between any two people, i and j, is visible to all other people in this group of N, and no other person in this group should be able to decode their communication. How many keys are needed in the system as a whole? For a sample scenario for this problem, if there are N=3 people, Bob, Alice, Trudy, then one symmetric key is shared by each pair: Bob-Alice, Alice-Trudy, Bob-Trudy, giving a total count of keys= 3. You need to give the general expression for N nodes, which must clearly also satisfy this example.