A plotter head scans a binary tree one level at a time in a back-and-forth (boustrophedon) pattern. Level 0 is read left to right, level 1 right to left, level 2 left to right again, and so on, alternating on every level. Concatenate the values in the order they are read into a single sequence.
Input format
Line 1: an integer n, the number of tokens on the next line.
Line 2: n space-separated tokens describing a binary tree in level-order (breadth-first). The first token is the root's value. Reading left to right, keep a queue of already-created nodes; for each node taken from the front of the queue, the next two tokens are its left child then its right child, where the token null marks a missing child. Only non-null children are added to the queue. Trailing null tokens for absent children at the deepest level may be omitted. Every node value is an integer.
Output format
A single line: all node values in boustrophedon (zigzag) order, space-separated.
Constraints
- 1 <= n <= 129
- The tree has at least 1 and at most 40 nodes.
- Each node value is an integer with -1000 <= value <= 1000.