Case 1: yes: 3 yes: 3 no yes: 2 0: 2 1: 4 2: 1 3: 1 0: 1 1: 1 2: 1 3: 2 4: 1 5: 2 yes: 3 0: 2 1: 4 2: 2 3: 2 0: 3 1: 5 2: 1 3: 1 yes: 0 no connections 0: 1 1: 3 2: 5 3: 1 4: 1 ----------