line  1: 0    -> 8 is the root
line  3: l    -> 4 is the left child of 8
line  5: l    -> 2 is the left child of 4
line  7: l    -> 1 is the left child of 2
line  9: ur   -> up 1 to 2, 3 is its right child
line 11: uur  -> up 2 to 4, 6 is its right child
line 13: l    -> 5 is the left child of 6
line 15: ur   -> up 1 to 6, 7 is its right child
line 17: uuur -> up 3 to 8, 12 is its right child
line 19: l    -> 10 is the left child of 12
line 21: l    -> 9 is the left child of 10
line 23: ur   -> up 1 to 10, 11 is its right child
line 25: uur  -> up 2 to 12, 14 is its right child
line 27: l    -> 13 is the left child of 14
line 29: ur   -> up 1 to 14, 15 is its right child
nodes: 15, height: 4
preorder : 8 4 2 1 3 6 5 7 12 10 9 11 14 13 15
inorder  : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
postorder: 1 3 2 5 7 6 4 9 11 10 13 15 14 12 8
sideways (root on the left, right children above):
                  15
            14
                  13
      12
                  11
            10
                  9
8
                  7
            6
                  5
      4
                  3
            2
                  1
