Case 1:
  Group 1: 1, 2
  Group 2: 3, 4
Case 2:
  Group 1: 3, 6
  Group 2: 4, 5
  Group 3: 1, 2
Case 3:
  Group 1: 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
           21, 22, 23, 24, 25
  Group 2: 3, 4
Case 4:
  Group 1: 1, 2, 7, 10, 13, 16, 19, 22, 25, 28
  Group 2: 3, 4, 8, 11, 14, 17, 20, 23, 26, 29
  Group 3: 5, 6, 9, 12, 15, 18, 21, 24, 27, 30